Nonlinear Time Series Analysis Research Articles

Detecting Metabolic Thresholds from Nonlinear Analysis of Heart Rate Time Series: A Review.

Heart rate time series are widely used to characterize physiological states and athletic performance. Among the main indicators of metabolic and physiological states, the detection of metabolic thresholds is an important tool in establishing training protocols in both sport and clinical fields. This paper reviews the most common methods, applied to heart rate (HR) time series, aiming to detect metabolic thresholds. These methodologies have been largely used to assess energy metabolism and to identify the appropriate intensity of physical exercise which can reduce body weight and improve physical fitness. Specifically, we focused on the main nonlinear signal evaluation methods using HR to identify metabolic thresholds with the purpose of identifying a method which can represent a useful tool for the real-time settings of wearable devices in sport activities. While the advantages and disadvantages of each method, and the possible applications, are presented, this review confirms that the nonlinear analysis of HR time series represents a solid, robust and noninvasive approach to assess metabolic thresholds.

The nonlinearity properties of pulse signal of pregnancy in the three trimesters

The purpose of this work sought to investigate the underlying activity state and dynamics characteristic changes of pulse in the three trimesters from healthy pregnant subjects by using nonlinear methods. Firstly, 176 healthy young pregnant women of different gestational ages were allocated for the study. The subjects were divided into three trimesters, namely first trimester, second trimester and third trimester, according to gestational age (8–12 weeks; 24–28 weeks; 32–36 weeks). Secondly, methods of nonlinear time series analysis, including phase-space reconstruction, time delay embedding, recurrence plot (RP), recurrence quantification analysis (RQA), Poincaré section and largest Lyapunov exponent (LLE) were applied to pulse time series to identify the unique characteristics of the pulse as a dynamical system. Finally, the natural complexity of pulse dynamics has been analyzed and assessed. The results demonstrated that (a) the predictability and regularity (DET: 97.499 vs. 98.471 vs. 98.319, p<0.05), stability (LMAX: 5874.167 vs. 9311.667 vs. 5733.833, p<0.05) and laminar states (LAM: 97.216 vs. 98.224 vs. 97.967, p<0.05) of three trimesters are significantly; (b) the long-term changes of pregnancy pulse in second trimester is significantly higher compared with the first and third trimesters (SD2: 1.0697 vs. 1.0747 vs. 1.0075, p<0.05); (c) the ability of subjects to respond to external stimuli gradually increases (λ: 0.752 vs. 0.768 vs. 0.782, p<0.05). The result of these analyses validates nonlinear characteristics of pulse with different gestation periods, while presence of significant difference has also been noticed. Additionally, the nonlinear methods are used to characterize the pulse changes during pregnancy from both qualitative and quantitative perspectives, which reveal important characteristics of biological signals. This gives us a good theoretical basis for the analysis and applied studies in Traditional Chinese Medicine(TCM).

Effect of Counter- and Co-Swirl on Low-Frequency Combustion Instabilities of Jet A-1 Spray Flames

Abstract The present article experimentally investigates the influence of pilot swirling directions on low-frequency combustion instabilities of pilot diffusion flames in a laboratory-scale combustor with jet A-1 fuel and air at atmospheric pressure. Airblast atomization nozzles with either counter-rotating (CTR) or corotating (COR) pilot swirl flows were examined using nonlinear time-series analyses and high-speed flame imaging measurements under idle and subidle operating conditions. We show that while the amplitude and frequency of limit cycle oscillations are observed to be similar for both cases, detailed examinations of measured experimental data reveal marked differences in stabilization mechanisms and pressure-heat release coupling processes. The spray flame dynamics subjected to counter-rotating swirl flows are governed by large-amplitude pressure oscillations, even under the influence of destructive pressure-heat release rate interference. The mechanism of destructive interference is closely related to the interactions between a spiral diffusion flame and a periodically detached reaction zone. Nonpremixed liquid-fueled flames involving corotating swirl, on the other hand, feature a more compact and intense reaction zone.

Methods of Nonlinear Time Series Cycle Analysis in Big Data Environment and IoT Application

There have been a lot of changes in nonlinear time series analysis techniques over the last few decades. They came from their time series background and have grown some of these techniques to try to fill in a gap in the ability to model and predict certain types of data, like chaotic and fixed systems. It is possible to find a lot of these systems all over different places in both natural and human worlds. This study explains how these techniques came to be, what they are based on, and how some of them can predict what will happen in the future. This study is trying to figure out how they work and what they could be used for. The contribution of this study is a different way to look at time series data. It looks at how the data is made and how big the time series is. Here, we talk about how the model comes together in terms of order. In this example, we look at the time series of the sectorial indices on the National Stock Exchange (India) to show that the model is getting close. Convergence also points out that, when we fit the same number of data points to the same model, we get the same thing every time. This shows that a true model correctly predicted the value of the future and that data always comes together in nature. A study found that the size of a big data time series should be taken into account when looking at the time series’ realization. This means that the DGP intervals for each study period can be the best representative intervals for that time period.

Fuzzy Dispersion Entropy: A Nonlinear Measure for Signal Analysis

Entropy is a powerful tool for nonlinear analysis of time series. We have recently introduced dispersion entropy (DispEn), which has widely drawn attention from researchers in a variety of settings in data analysis. However, DispEn is sensitive to its parameters, especially number of classes (quantization level). Additionally, in some cases, a small change in the signal amplitude due to noise changes the quantized series and so entropy value. To address these limitations, we develop fuzzy dispersion entropy (FuzzDispEn) on the basis of fuzzy membership functions for the quantization of a signal and Shannon entropy (ShEn). In FuzzDispEn, the concept of fuzzification in ShEn-based methods is introduced for the first time. Several straightforward concepts in signal processing using a set of time series were utilized to show the advantages of FuzzDispEn over DispEn in terms of the detection of the dynamical variability of signals. The results showed that FuzzDispEn has lower sensitivity to noise and signal length compared to DispEn. FuzzDispEn was also applied to five real world applications: mechanical fault detection in gearbox, fault diagnosis of rolling element bearings, damage level detection of bearings, detection of blood pressure in salt-sensitive rats, and detection of seizure and seizure-free electroencephalographics (EEGs). The results suggest that FuzzDispEn outperforms DispEn as well as popular sample entropy and permutation entropy in distinguishing different kinds of dynamical patterns in synthetic and real data.

Non-linear feature analysis of public emotion evolution for online teaching during the COVID-19 pandemic

PurposeNowadays, the breakout of the COVID-19 pandemic has caused an important change in teaching models. The emotional experience of this change has an important impact on online teaching. This paper aims to explore its time evolution characteristics and provide reference for the development of online teaching in the post epidemic era.Design/methodology/approachThe article firstly crawls the online teaching-related comment text data on Zhihu platform and performs emotional calculation to obtain a one-dimensional time series of daily average emotional values. Then, by using non-linear time-series analysis, this paper reconstructs the daily average emotion value time series in high-dimensional phase space, calculates the maximum Lyapunov exponent and correlation dimension and finally, explores the feature patterns through recurrence plot and recurrence quantification analysis.FindingsIt was found that the sequence has typical non-linear chaotic characteristics; its correlation dimension indicates that it contains obvious fractal characteristics; the public emotional evolution shows a cyclical rise and fall. By text mining and temporal evolution analysis, this paper explores the evolution law over chronically of the daily average emotion value time series, provides feasible strategies to improve students' online learning experience and quality and continuously optimizes this new teaching model in the era of pandemic.Originality/valueBased on social knowledge sharing platform of Q&A, this paper models and analyzes users interaction data under online teaching-related topics. This paper explores the evolution law over a long time period of the daily average emotion value time series using text mining and temporal evolution analysis. It then offers workable solutions to enhance the quality and experience of students' online learning, and it continuously improves this new teaching model in the age of pandemics.

Searching for Chaotic Behavior in the Ion Current Waveforms of a Hall Effect Thruster

The dynamics of the ion flux expelled by a 0.5 kW-class Hall thruster supplied with krypton was examined in a wide range of discharge voltages. A homemade Faraday probe installed onto a rotary arm was used for reconstructing angular profiles of the plasma plume 0.5 m downstream of the thruster exit plane. The time dependence of the ion current was measured along the thruster axis. For investigating the signal dynamics, a Fourier approach as well as methods of nonlinear time series analysis like bifurcation diagrams and recurrence plot techniques were applied, which are of interest for chaotic behavior identification. Along with the well-known breathing mode (10—30 kHz), other characteristic groups of oscillations were also detected. The bifurcation diagram revealed a drastic transition between large and small amplitude oscillating regimes while varying the discharge voltage from 550 to 700 V. In parallel to this transition, recurrent plots display a qualitative change from a periodic (or quasi periodic) oscillating regime to much less predictable dynamics.

Reconstruction of a Soil Microbial Network Induced by Stress Temperature.

ABSTRACTThe microbial community is viewed as a network of diverse microorganisms connected by various interspecific interactions. While the stress gradient hypothesis (SGH) predicts that positive interactions are favored in more stressful environments, the prediction has been less explored in complex microbial communities due to the challenges of identifying interactions. Here, by applying a nonlinear time series analysis to the amplicon-based diversity time series data of the soil microbiota cultured under less stressful (30°C) or more stressful (37°C) temperature conditions, we show how the microbial network responds to temperature stress. While the genera that persisted only under the less stressful condition showed fewer positive effects, the genera that appeared only under the more stressful condition received more positive effects, in agreement with SGH. However, temperature difference also induced reconstruction of the community network, leading to an increased proportion of negative interactions at the whole-community level. The anti-SGH pattern can be explained by the stronger competition caused by increased metabolic rate and population densities.IMPORTANCE By combining amplicon-based diversity survey with recently developed nonlinear analytical tools, we successfully determined the interaction networks of more than 150 natural soil microbial genera under less or more temperature stress and explored the applicability of the stress gradient hypothesis to soil microbiota, shedding new light on the well-known hypothesis.

THE TWIN DEFICITS OR NEGATIVE REVERSE CAUSALITY? A NONLINEAR APPROACH TO THE TURKISH BUDGET AND CURRENT ACCOUNT BALANCES

The budget deficit causing an increase in the current account deficit is named twin deficits. In addition, the budget and current account balances represent the internal and external balance of the economy. As in many developed and developing countries, revealing the relationship between internal and external imbalances in the Turkish economy in terms of determining economic policies is very important. Most of the studies on twin deficits in the literature are based on analyzes with linear models. The aim of this study, unlike other studies in the literature, is to examine the relationship between the budget and current account balance in the Turkish economy with non-linear time series analysis. For this purpose, nonlinear unit root and cointegration tests were applied to the data covering the period 1994-2021. The findings show that the negative reverse causality hypothesis is valid instead of the twin deficits hypothesis in the Turkish economy in the analyzed period. Accordingly, there is a negative relationship from the current account balance to the budget balance in both the long and short run.

Experimental Diagnosis on Combustion Characteristic of Shock Wave Focusing Initiation Engine.

A shock wave focusing initiation engine was assembled and tested in an experimental program. The effective pyrolysis rate of the pre-combustor was evaluated over a range of supplementary fuel ratio in this paper. Results highlight two operational modes of the resonant cavity: (1) pulsating combustion mode, (2) stable combustion mode. The appearance of the two combustion modes is jointly affected by the flow and the structural characteristic value of the combustion chamber. This paper uses images, time-frequency analysis, and nonlinear time series analysis methods to identify and distinguish these two combustion modes. It is believed that the interaction between the combustion chamber and the supply plenum is the probable reason for different combustion modes. The experiment has found that structural parameters and import flow parameters have an impact on the initiation of the combustion chamber. Increasing the injection pressure can appropriately broaden the fuel-rich boundary of initiation. Low equivalence ratio and high injection pressure can also appropriately increase the combustion working frequency in a small range. From the perspective of pressure utilization, under the premise of ensuring successful initiation, injection pressure should not be too high.

Photoplethysmogram Recording Length: Defining Minimal Length Requirement from Dynamical Characteristics.

Photoplethysmography is a widely used technique to noninvasively assess heart rate, blood pressure, and oxygen saturation. This technique has considerable potential for further applications—for example, in the field of physiological and mental health monitoring. However, advanced applications of photoplethysmography have been hampered by the lack of accurate and reliable methods to analyze the characteristics of the complex nonlinear dynamics of photoplethysmograms. Methods of nonlinear time series analysis may be used to estimate the dynamical characteristics of the photoplethysmogram, but they are highly influenced by the length of the time series, which is often limited in practical photoplethysmography applications. The aim of this study was to evaluate the error in the estimation of the dynamical characteristics of the photoplethysmogram associated with the limited length of the time series. The dynamical properties were evaluated using recurrence quantification analysis, and the estimation error was computed as a function of the length of the time series. Results demonstrated that properties such as determinism and entropy can be estimated with an error lower than 1% even for short photoplethysmogram recordings. Additionally, the lower limit for the time series length to estimate the average prediction time was computed.

On Fourier phases and their relevance for nonlinear time series analysis

Many processes in nature are governed by nonlinear mechanisms that are frequently superposed by pronounced linear components. To characterize such complex dynamics it is desirable to disentangle linear and nonlinear features in empirical data. Quantitative nonlinear measures are also influenced by linear properties of the signals and, for the univariate case, Fourier transform surrogates do not represent properly the null hypothesis of zero nonlinear features. Here we elaborate on the application of a recently published method in Fourier space that does not suffer from comparison with inappropriate surrogate data and that reveals with high sensitivity correlations between Fourier phases and amplitudes. In addition, we propose a simple pre-processing procedure that avoids the mixing of linear and nonlinear features when applying conventional nonlinear measures, which can drastically increase the sensitivity of the statistical evaluation and avoids numerical problems associated with surrogate data. We test our proposal on data derived from numerical models and we analyze electroencephalographic recordings from epilepsy patients as well as heart rate signals from healthy subjects before and during meditation.

NoLiTiA: An Open-Source Toolbox for Non-linear Time Series Analysis.

In many scientific fields including neuroscience, climatology or physics, complex relationships can be described most parsimoniously by non-linear mechanics. Despite their relevance, many neuroscientists still apply linear estimates in order to evaluate complex interactions. This is partially due to the lack of a comprehensive compilation of non-linear methods. Available packages mostly specialize in only one aspect of non-linear time-series analysis and most often require some coding proficiency to use. Here, we introduce NoLiTiA, a free open-source MATLAB toolbox for non-linear time series analysis. In comparison to other currently available non-linear packages, NoLiTiA offers (1) an implementation of a broad range of classic and recently developed methods, (2) an implementation of newly proposed spatially and time-resolved recurrence amplitude analysis and (3) an intuitive environment accessible even to users with little coding experience due to a graphical user interface and batch-editor. The core methodology derives from three distinct fields of complex systems theory, including dynamical systems theory, recurrence quantification analysis and information theory. Besides established methodology including estimation of dynamic invariants like Lyapunov exponents and entropy-based measures, such as active information storage, we include recent developments of quantifying time-resolved aperiodic oscillations. In general, the toolbox will make non-linear methods accessible to the broad neuroscientific community engaged in time series processing.

Causal Inference in Time Series in Terms of Rényi Transfer Entropy.

Uncovering causal interdependencies from observational data is one of the great challenges of a nonlinear time series analysis. In this paper, we discuss this topic with the help of an information-theoretic concept known as Rényi’s information measure. In particular, we tackle the directional information flow between bivariate time series in terms of Rényi’s transfer entropy. We show that by choosing Rényi’s parameter , we can appropriately control information that is transferred only between selected parts of the underlying distributions. This, in turn, is a particularly potent tool for quantifying causal interdependencies in time series, where the knowledge of “black swan” events, such as spikes or sudden jumps, are of key importance. In this connection, we first prove that for Gaussian variables, Granger causality and Rényi transfer entropy are entirely equivalent. Moreover, we also partially extend these results to heavy-tailed -Gaussian variables. These results allow establishing a connection between autoregressive and Rényi entropy-based information-theoretic approaches to data-driven causal inference. To aid our intuition, we employed the Leonenko et al. entropy estimator and analyzed Rényi’s information flow between bivariate time series generated from two unidirectionally coupled Rössler systems. Notably, we find that Rényi’s transfer entropy not only allows us to detect a threshold of synchronization but it also provides non-trivial insight into the structure of a transient regime that exists between the region of chaotic correlations and synchronization threshold. In addition, from Rényi’s transfer entropy, we could reliably infer the direction of coupling and, hence, causality, only for coupling strengths smaller than the onset value of the transient regime, i.e., when two Rössler systems are coupled but have not yet entered synchronization.

Data-based modeling and identification for general nonlinear dynamical systems by the multidimensional Taylor network

PurposeThe present study is intended to develop an effective approach to the real-time modeling of general dynamic nonlinear systems based on the multidimensional Taylor network (MTN).Design/methodology/approachThe authors present a detailed explanation for modeling the general discrete nonlinear dynamic system by the MTN. The weight coefficients of the network can be obtained by sampling data learning. Specifically, the least square (LS) method is adopted herein due to its desirable real-time performance and robustness.FindingsCompared with the existing mainstream nonlinear time series analysis methods, the least square method-based multidimensional Taylor network (LSMTN) features its more desirable prediction accuracy and real-time performance. Model metric results confirm the satisfaction of modeling and identification for the generalized nonlinear system. In addition, the MTN is of simpler structure and lower computational complexity than neural networks.Research limitations/implicationsOnce models of general nonlinear dynamical systems are formulated based on MTNs and their weight coefficients are identified using the data from the systems of ecosystems, society, organizations, businesses or human behavior, the forecasting, optimizing and controlling of the systems can be further studied by means of the MTN analytical models.Practical implicationsMTNs can be used as controllers, identifiers, filters, predictors, compensators and equation solvers (solving nonlinear differential equations or approximating nonlinear functions) of the systems of ecosystems, society, organizations, businesses or human behavior.Social implicationsThe operating efficiency and benefits of social systems can be prominently enhanced, and their operating costs can be significantly reduced.Originality/valueNonlinear systems are typically impacted by a variety of factors, which makes it a challenge to build correct mathematical models for various tasks. As a result, existing modeling approaches necessitate a large number of limitations as preconditions, severely limiting their applicability. The proposed MTN methodology is believed to contribute much to the data-based modeling and identification of the general nonlinear dynamical system with no need for its prior knowledge.

Identifying Targets for Antibiotic Use for the Management of Carbapenem-Resistant Acinetobacter baumannii (CRAb) in Hospitals-A Multi-Centre Nonlinear Time-Series Study.

Solutions are needed to inform antimicrobial stewardship (AMS) regarding balancing the access to effective antimicrobials with the need to control antimicrobial resistance. Theoretical and mathematical models suggest a non-linear relationship between antibiotic use and resistance, indicating the existence of thresholds of antibiotic use beyond which resistance would be triggered. It is anticipated that thresholds may vary across populations depending on host, environment, and organism factors. Further research is needed to evaluate thresholds in antibiotic use for a specific pathogen across different settings. The objective of this study is to identify thresholds of population antibiotic use associated with the incidence of carbapenem-resistant Acinetobacter baumannii (CRAb) across six hospital sites in Oman. The study was an ecological, multi-centre evaluation that involved collecting historical antibiotic use and CRAb incidence over the period from January 2015 to December 2019. By using non-linear time-series analysis, we identified different thresholds in the use of third-generation cephalosporins, piperacillin-tazobactam, aminoglycoside, and fluoroquinolones across participating hospitals. The identification of different thresholds emphasises the need for tailored analysis based on modelling data from each hospital. The determined thresholds can be used to set targets for each hospital AMS, providing a balance between access to these antibiotics versus controlling CRAb incidence.

Fractal and Time-series A nalyses based Rhonchi and Bronchial Auscultation: A Machine Learning Approach

Objectives: The present work reports the study of 34 rhonchi (RB) and Bronchial Breath (BB) signals employing machine learning techniques, time-frequency, fractal, and non-linear time-series analyses. Methods: The time-frequency analyses and the complexity in the dynamics of airflow in BB and RB are studied using both Power Spectral Density (PSD) features and non-linear measures. For accurate prediction of these signals, PSD and non-linear measures are fed as input attributes to various machine learning models. Findings: The spectral analyses reveal fewer, low-intensity frequency components along with its overtones in the intermittent and rapidly damping RB signal. The complexity in the dynamics of airflow in BB and RB is investigated through the fractal dimension, Hurst exponent, phase portrait, maximal Lyapunov exponent, and sample entropy values. The greater value of entropy for the RB signal provides an insight into the internal morphology of the airways containing mucous and other obstructions. The Principal Component Analysis (PCA) employs PSD features, and Linear Discriminant Analysis (LDA) along with Pattern Recognition Neural Network (PRNN) uses non-linear measures for predicting BB and RB. Signal classification based on phase portrait features evaluates the multidimensional aspects of signal intensities, whereas that based on PSD features considers mere signal intensities. The principal components in PCA cover about 86.5% of the overall variance of the data class, successfully distinguishing BB and RB signals. LDA and PRNN that use non-linear time-series parameters identify and predict RB and BB signals with 100% accuracy, sensitivity, specificity, and precision. Novelty: The study divulges the potential of non-linear measures and PSD features in classifying these signals enabling its application to be extended for low-cost, non-invasive COVID-19 detection and real-time health monitoring. Keywords: lung signal, fractal analysis, sample entropy, non­linear time­series, machine learning techniques

How does genetic architecture affect eco-evolutionary dynamics? A theoretical perspective.

Recent studies have revealed the importance of feedbacks between contemporary rapid evolution (i.e. evolution that occurs through changes in allele frequencies) and ecological dynamics. Despite its inherent interdisciplinary nature, however, studies on eco-evolutionary feedbacks have been mostly ecological and tended to focus on adaptation at the phenotypic level without considering the genetic architecture of evolutionary processes. In empirical studies, researchers have often compared ecological dynamics when the focal species under selection has a single genotype with dynamics when it has multiple genotypes. In theoretical studies, common approaches are models of quantitative traits where mean trait values change adaptively along the fitness gradient and Mendelian traits with two alleles at a single locus. On the other hand, it is well known that genetic architecture can affect short-term evolutionary dynamics in population genetics. Indeed, recent theoretical studies have demonstrated that genetic architecture (e.g. the number of loci, linkage disequilibrium and ploidy) matters in eco-evolutionary dynamics (e.g. evolutionary rescue where rapid evolution prevents extinction and population cycles driven by (co)evolution). I propose that theoretical approaches will promote the synthesis of functional genomics and eco-evolutionary dynamics through models that combine population genetics and ecology as well as nonlinear time-series analyses using emerging big data.This article is part of the theme issue ‘Genetic basis of adaptation and speciation: from loci to causative mutations’.

Phase portrait and fractal analyses in nanobiophotonics: carbon nanoparticle aided intra-pigment energy transfer in leaves

The paper delineates the potential application of nonlinear time series analysis (TSA) in Nanobiophotonics to explore the soot-assisted intra-pigment energy transport mechanism in leaves. The soot nanofluid, containing nano carbon allotropes, prepared in different concentrations, is sprayed over Lablab purpureus (L.) sweet leaves. The chlorophyll extracted from the leaves after ten days is subjected to UV-Visible absorption and single beam thermal lens (TL) studies. The variation of the absorbance of signature peaks of chlorophyll pigments with the soot concentration reveals the role of soot in the intra-pigment energy transport, divulged through the time series TL signal. The TSA of the TL signals, the plotting of phase portraits, and the computation of sample entropy (S), fractal dimension (FD), and Hurst exponent for the pigment-soot systems unwrap the particle/molecular dynamics and the flow of energy within the system. The analysis by segmenting the variations of the TSA measures with soot concentration reveals that the values of S and FD of the system are high in the low and high concentration ranges, in agreement with the randomness reflected in the phase portrait. The middle region, where S and FD decrease, seems more energy-efficient for the photosystem through heat trap and energy exchange between the pigment-soot system. The study gives information about the critical concentration range suitable for increased photosynthesis in leaves and yield enhancement.

Multi-scale transition network approaches for nonlinear time series analysis

Complex networks are powerful tools for nonlinear time series analysis, which are undergoing fast development in the recent decade. Here we propose a novel way to construct multi-scale transition networks from time series, which are based on coarse-graining partitions of phase space. Using time series from both discrete Hénon map and continuous Rössler systems, we demonstrate that the multi-scale transition entropy values of the resulting networks show the same power as the Lyapunov exponents, identifying chaotic transitions successfully. The advantage is that our method works successfully when only a small number of 3–5 bins is used for the partition generation, while the traditional static node entropy measures work poorly. Further experimental examples in fMRI and ECG analysis show that these entropy measures are able to characterizing different rhythmic states of subjects, showing high potential for time series analysis from complex systems.