Nonlinear Time Series Analysis Research Articles

Nonlinear time series analysis unravels underlying mechanisms of interspecific synchrony among foliage‐feeding forest Lepidoptera species

AbstractInterspecific synchrony, that is, synchrony in population dynamics among sympatric populations of different species can arise via several possible mechanisms, including common environmental effects, direct interactions between species, and shared trophic interactions, so that distinguishing the relative importance of these causes can be challenging. In this study, to overcome this difficulty, we combine traditional correlation analysis with a novel framework of nonlinear time series analysis, empirical dynamic modeling (EDM). The EDM is an analytical framework to identify causal relationships and measure changing interaction strength from time series. We apply this approach to time series of sympatric foliage‐feeding forest Lepidoptera species in the Slovak Republic and yearly mean temperature, precipitation and North Atlantic Oscillation Index. These Lepidoptera species include both free‐feeding and leaf‐roller larval life histories: the former are hypothesized to be more strongly affected by similar exogenous environments, while the latter are isolated from such pressures. Correlation analysis showed that interspecific synchrony is generally strongest between species within same feeding guild. In addition, the convergent cross mapping analysis detected causal effects of meteorological factors on most of the free‐feeding species while such effects were not observed in the leaf‐rolling species. However, there were fewer causal relationships among species. The multivariate S‐map analysis showed that meteorological factors tend to affect similar free‐feeding species that are synchronous with each other. These results indicate that shared meteorological factors are key drivers of interspecific synchrony among members of the free‐feeding guild, but do not play the same role in synchronizing species within the leaf‐roller guild.

2443. Impact of Antimicrobial Stewardship on the Incidence of Carbapenem-Resistant Pseudomonas aeruginosa: A Nonlinear Time-Series Analysis Approach to Identify Carpapenem Thresholds

BackgroundTo estimate the impact of antimicrobials stewardship in the temporary evolution of the Density Incidence of Pseudomonas aeruginosa resistant to carbapenems (DI_PaCRE).MethodsIn Modena Policlinico, a tertiary care hospital, from September 2014, universal rectal screening and antibiotic stewardship (ABS) focusing on carbapenem sparing strategy were introduced. We used the statistical approach already described (A nonlinear time-series analysis approach to identify thresholds in associations between population antibiotic use and rates of resistance. López-Lozano JM, et al. Nat Microbiol. 2019 Apr 8. doi: 10.1038/s41564-019–0410-0) in order to adjust a non-linear model (Multivariate Adaptive Regression Splines) looking for the identification and estimation of thresholds in the influence of the use of Carbapenems on the DI_PaCRE.ResultsWe identified a threshold at 5.65 DDD/100 bed-days of Carbapenems (CarbUse). Indeed, above this threshold, for every increase of one DDD/100 bed-days, the DI_PaCRE increased by 0.15 new cases by 1000 bed-days. On the basis of our analyses, considering a typical course of 7 days of treatment, an average CarbUse of 6.5 DDD/100 bed-days in 2012 and 2013, for an average of 15000 monthly bed-days, means around 139 treated patients. In order to avoid the emergence of resistance, the threshold was equivalent to a maximum number of 121 patients to be treated. Below this threshold, i.e in 2018, CarbUse including 66 patients treated did not select antimicrobial resistance.ConclusionPaCRE could be controlled by reducing the use of carbapenems below minimum thresholds of 6.5 DDD/100 bed-days. In order to avoid the onset of resistance to carbapenems in Pseudomonas aeruginosa, less than 121 patients per month should receive this class of drug. This finding could provide innovative approach to guide antimicrobial stewardship strategy focused on limit the spread of PaCRE in hospital populations. Disclosures All authors: No reported disclosures.

Teaching Ordinal Patterns to a Computer: Efficient Encoding Algorithms Based on the Lehmer Code

Ordinal patterns are the common basis of various techniques used in the study of dynamical systems and nonlinear time series analysis. The present article focusses on the computational problem of turning time series into sequences of ordinal patterns. In a first step, a numerical encoding scheme for ordinal patterns is proposed. Utilising the classical Lehmer code, it enumerates ordinal patterns by consecutive non-negative integers, starting from zero. This compact representation considerably simplifies working with ordinal patterns in the digital domain. Subsequently, three algorithms for the efficient extraction of ordinal patterns from time series are discussed, including previously published approaches that can be adapted to the Lehmer code. The respective strengths and weaknesses of those algorithms are discussed, and further substantiated by benchmark results. One of the algorithms stands out in terms of scalability: its run-time increases linearly with both the pattern order and the sequence length, while its memory footprint is practically negligible. These properties enable the study of high-dimensional pattern spaces at low computational cost. In summary, the tools described herein may improve the efficiency of virtually any ordinal pattern-based analysis method, among them quantitative measures like permutation entropy and symbolic transfer entropy, but also techniques like forbidden pattern identification. Moreover, the concepts presented may allow for putting ideas into practice that up to now had been hindered by computational burden. To enable smooth evaluation, a function library written in the C programming language, as well as language bindings and native implementations for various numerical computation environments are provided in the supplements.

GRAPHICAL METHODS FOR NON-LINEAR ANALYSIS OF ELECTROCARDIOGRAPHIC DATA

INTRODUCTION: One of the most widely used methods for studying the bioelectric activity of the heart is the electrocardiogram (ECG). An important diagnostic parameter that can be determined by the ECG is heart rate variability (HRV), which takes into account the difference between successive strokes of the heart. Changing HRV can be an indicator of a number of disease states, such as low HRV levels can show poor health that is not only associated with cardiovascular disease but also with other diseases such as internal, nervous, mental, and other disorders.
 OBJECTIVES: The subject of this article is the study of 24-hour ECG signals by applying non-linear graphical methods for HRV analysis. The non-linear graphical methods aim at obtaining graphical and quantitative information on the cardiovascular status of the study groups to complement the information obtained from traditional linear methods of analysis.
 METHODS: For the non-linear analysis of HRV, graphical methods were used: Poincaré plot and Recurrence plot were used, which are suitable for the examination of electrocardiographic signals. Two groups of people were investigated: 20 healthy controls and 20 patients with arrhythmia.
 RESULTS: Based on the nonlinear analysis of RR time series, the graphs of a healthy subject and a patient with arrhythmia were constructed using the Poincare plot. The graph of the healthy subject has the shape of a comet, while the graph of the patient with arrhythmia has the shape of a fan. The quantitative characteristics of patients with arrhythmia significantly change compared to the healthy subjects. The SD1 (p <0.003) and SD2 (p <0.0001) values decreased in patients with arrhythmia compared to the healthy controls. This reduction leads to reduction of the areas of the ellipse in the patients with arryhthmia. The ratio of SD1/SD2 (p <0.05) is lower for the healthy controls. The graphs obtained by the Recurrence plot of the investigated signals differ in healthy subjects and in patients with arrhythmia. For a healthy subject, the graph has a diagonal line and fewer squares showing a higher HRV. The graph of a patient with arrhythmia contains more squares, indicating periodicity in the investigated signal. The Recurrence Quantification Analysis showed that the values of the investigated parameters DET% (p <0.0001), REC% (p <0.0001) and ENTR (p <0.001) in patients with arrhythmia are increased.
 CONCLUSIONS: The importance of the graphical nonlinear methods used for the analysis of HRV consists in forming a parametric and graphical assessment of the patient's health status.

Nonlinear time series analysis by means of complex networks

In the last decade, there has been a growing body of literatures addressing the utilization of complex network methods for the characterization of dynamical systems based on time series, which has allowed addressing fundamental questions regarding the structural organization of nonlinear dynamics as well as the successful treatment of a variety of applications from a broad range of disciplines. In this report, we provide an in-depth review of three existing approaches of recurrence networks, visibility graphs and transition networks, covering their methodological foundations, interpretation and the recent developments. The overall aim of this report is to provide the Chinese readers with the future directions of time series network approaches and how the complex network approaches can be applied to their own field of real-world time series analysis.

Methodology for production logging in oil-in-water flows under low flow rate and high water-cut conditions

This study aimed to obtain the production profiles of oil-in-water flow under low flow rate and high water-cut conditions in oil wells. A combination production profile logging composed of an arc-type conductance sensor (ATCS) and a cross-correlation flow meter (CFM) with a center body is proposed and experimentally evaluated. The ATCS is designed for water holdup measurement, whereas the CFM with a center body is proposed to obtain the mixture velocity. Then, a drift-flux model based on flow patterns is established to predict the individual-phase superficial velocity of oil-in-water flows. Results show that the ATCS possesses high resolution in water holdup measurement and that flow pattern information can be deduced from its signal through nonlinear time series analysis. The CFM can enhance the correlation of upstream and downstream signals and simplify the relationship between the cross-correlation velocity and mixture velocity. On the basis of the drift-flux model, individual-phase superficial velocities can be predicted with high accuracy for different flow patterns.

Twisty Takens: a geometric characterization of good observations on dense trajectories

In nonlinear time series analysis and dynamical systems theory, Takens’ embedding theorem states that the sliding window embedding of a generic observation along trajectories in a state space, recovers the region traversed by the dynamics. This can be used, for instance, to show that sliding window embeddings of periodic signals recover topological loops, and that sliding window embeddings of quasiperiodic signals recover high-dimensional torii. However, in spite of these motivating examples, Takens’ theorem does not in general prescribe how to choose such an observation function given particular dynamics in a state space. In this work, we state conditions on observation functions defined on compact Riemannian manifolds, that lead to successful reconstructions for particular dynamics. We apply our theory and construct families of time series whose sliding window embeddings trace tori, Klein bottles, spheres, and projective planes. This greatly enriches the set of examples of time series known to concentrate on various shapes via sliding window embeddings, and will hopefully help other researchers in identifying them in naturally occurring phenomena. We also present numerical experiments showing how to recover low dimensional representations of the underlying dynamics on state space, by using the persistent cohomology of sliding window embeddings and Eilenberg–MacLane (i.e. circular and real projective) coordinates.

Investment Sustained by Consumption: A Linear and Nonlinear Time Series Analysis

This paper studies the dynamic relationship between consumption and investment in the United States between 1947 and 2018. Our findings support the postulates of Keynesian economics—while they are contrary to the theoretic background on which the numerous empirical studies on the saving-investment nexus are based. We find a long-run nexus between consumption and investment, and positive linear Granger-causality running unidirectionally from consumption to investment. Therefore, investment is sustained by consumption. Further, we find that the variables have nonlinear structures and, thus, we apply nonlinear causality tests. We provide evidence of nonlinear causality running unidirectionally from consumption to investment. Nevertheless, after controlling for Government Expenditure, this nonlinear causal relationship disappears, indicating that Government Expenditure drives the nonlinear causal relationship between private consumption and investment. We argue that this finding is consistent with the notion that investment decisions are guided by permanent aggregate demand, because public expenditure allows private consumption to have a sufficiently permanent trajectory to be considered as a guide for investment decisions. Our results do not support the austerity and deflation measures implemented in the last years (especially in the European Union). On the other hand, our findings call for the incentive of final public expenditure, since it favours the long-run link between the private decisions to consume and invest.

Pattern identification for wind power forecasting via complex network and recurrence plot time series analysis

Renewable energy sources, where wind energy is an important part, are increasingly participating in developing economies and environmental benefits. Wind power is strongly dependent on wind velocity and thus identifying patterns in wind speed data is an important issue for forecasting the generated power from a wind turbine and it has significant importance for the renewable energy market operations. In this work we approach the problem of identification of the underlying dynamic characteristics and patterns of wind behavior using two approaches of non-linear time series analysis tools: Recurrence Plots (RPs) and Complex Network analysis. The proposed methodology is applied on wind time series collected by cup anemometers located on a wind turbine installed in Greece. We show that the proposed approach provides useful information which can characterize distinct two time intervals of the data, one ranging from 2 to 4.5 days and another from 5 to 8.5 days. Also analysis can identify and detect dynamical transitions in the system's behavior and also reveals information about the changes in state inside the whole time series. The results will be useful in wind markets, for the prediction of the produced wind energy and also will be helpful for wind farm site selection.

Machine Learning of Time Series Using Time-Delay Embedding and Precision Annealing.

Tasking machine learning to predict segments of a time series requires estimating the parameters of a ML model with input/output pairs from the time series. We borrow two techniques used in statistical data assimilation in order to accomplish this task: time-delay embedding to prepare our input data and precision annealing as a training method. The precision annealing approach identifies the global minimum of the action (). In this way, we are able to identify the number of training pairs required to produce good generalizations (predictions) for the time series. We proceed from a scalar time series and, using methods of nonlinear time series analysis, show how to produce a -dimensional time-delay embedding space in which the time series has no false neighbors as does the observed time series. In that -dimensional space, we explore the use of feedforward multilayer perceptrons as network models operating on -dimensional input and producing -dimensional outputs.

Detecting nonlinear stochastic systems using two independent hypothesis tests.

Various systems in the real world can be nonlinear and stochastic, but because nonlinear time series analysis has been developed to distinguish nonlinear deterministic systems from linear stochastic systems, there have been no appropriate methods developed so far for testing the nonlinear stochasticity for a given system. Thus, here we propose a set of two hypothesis tests, one for the nonlinearity and one for the stochasticity, independent of each other. The test for the linearity is based on Fourier-transform-based surrogate data with a nonlinear test statistic, while the test for determinism depends on the theory of ordinal patterns or permutations recently developed intensively. We demonstrate the proposed set of tests with time series generated from toy models. In addition, we show that both a foreign exchange market and a temperature series in Tokyo could be nonlinear and stochastic, as well as sometimes with determinism beyond pseudoperiodicity.

Detection of self-organized criticality behavior in an electronic circuit designed to solve a third order non-linear ODE (NL-ODE) for a damped KdV equation.

In this work, we present an electronic implementation of a damped Korteweg-de Vries equation modeled as a third order nonlinear autonomous ordinary differential equation (jerk equation). The circuit has been realized using operational amplifiers, multipliers, and passive electronic components which provides the time series solution of the equation in agreement with the numerical simulation results. Using nonlinear time series analysis on the acquired waveform data, we have obtained different types of phase space portraits and further analysis reflected long range correlation in the chaotic time series. Important findings include hysteresis induced bifurcation and self-organized criticality behavior in the system which is mentioned in this work.

Chaos prediction and control based on time series analysis

The nonlinear time-series analysis method is used to study the nonlinear large-scale measurement system and the discrete nonlinear system. For the instability of the linear steady-scale large-scale pulse system, a class of discrete Lipschitz nonlinear system dimensionality observer is used. The suboptimal control method for chaotic discrete systems with time-delay is obtained. The mathematical model of the large-scale pulsed system and the nonlinear discrete system is established. The instability of the large-scale steady-turbulence-type impulsive large-scale system is discussed by using the concept of the metric impulse system. The chaos of the nonlinear large-scale pulsating large-scale system with perturbation is proved by using the Lyapunov V function and the comparison principle. Bifurcation, using differential dynamic programming method to transform the suboptimal control problem of nonlinear discrete systems with time delay into the optimal control problem of nonlinear discrete systems without time delay, and realize the control of chaos.

The paradox of re‐oligotrophication: the role of bottom–up versus top–down controls on the phytoplankton community

Increases in phytoplankton biomass have been widely observed over the past decades, even in lakes experiencing nutrient reduction. However, the mechanisms giving rise to this trend remain unclear. Here, we unveil the potential mechanisms through quantifying the relative contribution of bottom–up versus top–down control in determining biomasses of phytoplankton assemblages in Lake Geneva. Specifically, we apply nonlinear time series analysis, convergent cross mapping (CCM), to decipher the degree of bottom–up versus top–down control among phytoplankton assemblages via quantifying 1) causal links between environmental factors and various phytoplankton assemblages and 2) the relative importance of bottom–up, top–down, and environmental effects. We show that the recent increase in total phytoplankton biomass, albeit with phosphorus reduction, was mainly caused by a particular phytoplankton assemblage which was better adapted to the re‐oligotrophicated environment characterized by relatively low phosphorus concentrations and warm water temperature, and poorly controlled by zooplankton grazing. Our findings suggest that zooplankton act as a critical driver of phytoplankton biomass and strongly impact the dynamics of recovery from eutrophication. Therefore, our phytoplankton assemblage approach in combination with causal identification of top–down versus bottom–up controls provides insights into the reason why phytoplankton biomass may increase in lakes undergoing phosphorus reduction.

Model-free time series analysis detected the contributions of middle-age spawner biomass and the environment on Pacific bluefin tuna recruitment

Abstract The relationship between the biomass of Pacific bluefin tuna (PBF) spawners and the amount of recruitment (stock–recruitment relationship, SRR) is unclear. It is likely that environmental effects have masked the SRR of PBF. As the basis of constructing an effective SRR for PBF, we examined the effect of spawning biomass at different ages and the spatiotemporal patterns of environmental effects on the amount of recruitment, using a recently developed model-free nonlinear time series analysis method (empirical dynamic modelling, EDM). EDM revealed where, when, and how the environment affected the amount of recruitment. EDM also found a significant contribution of ages 8–9 spawners on recruitment dynamics and that the amount of recruitment plateaus with increase in ages 8–9 spawners. Based on knowledge obtained from EDM, we formulated several example SRRs that incorporated environmental effects (sea surface temperature). The newly developed SRR with information from EDM outperformed the SRR without this information. Finally, we interpreted the results based on preceding observational and experimental studies and discussed the potential of applying the combination of EDM and mathematical modelling towards the sustainable use of other stocks.

KarsTS: an R package for microclimate time series analysis

KarsTS 2.2 is free, open-source, R-based software for microclimate time series, especially suited to the study of underground or highly insulated environments. The time series of interest include air temperature, humidity, and CO2 and 222Rn content, amongst others. These time series usually pose problems such as gaps, outliers, noise or relative shortness. KarsTS was born as a package for gap filling and thus, it offers multiple univariate and multivariate gap-filling tools well suited to these variables. However, as KarsTS was intended to be a self-sufficient program, it soon grew to encompass several tools for linear and nonlinear time series analysis, preprocessing and plotting. Indeed, many of these variables show a nonlinear behavior that is often disregarded; for this reason, we aim to spread and facilitate the use of some methodologically appropriate analysis tools, even amongst researcher that do not feel comfortable using a console. In this paper, we introduce an overview of KarsTS functionality and we show its potential through some practical application examples on four-year time series of temperature from the Rull cave (Spain).

Nonlinear Economic Time Series as a Testbed for Dynamic Macro Models Including Finance

This is consequent upon an earlier paper of mine (Non linear economic time series as a test bed for dynamic macro models) which was an exercise in using nonlinear time series analysis (NLTS) to assess the fit of a dynamic nonlinear macro economic process, the Goodwin model, against “realworld” nonlinear time series. This paper extends that approach to address models which include Finance and Debt as variables. Notably the work of Professor S Keen, This, Finance and Debt, is something notably missing from Goodwin’s models.

NONLINEAR TIME SERIES ANALYSIS USING ORDINAL NETWORKS WITH SELECT APPLICATIONS IN BIOMEDICAL SIGNAL PROCESSING

NONLINEAR TIME SERIES ANALYSIS USING ORDINAL NETWORKS WITH SELECT APPLICATIONS IN BIOMEDICAL SIGNAL PROCESSING

Revealing transitions in friction-excited vibrations by nonlinear time-series analysis

We study the transitions in friction-induced vibrations (FIV) experimentally. The measurement data stem from a highly sophisticated setup specifically designed to study FIV problems and where the relative motion between the samples is achieved using air bearings and a voice-coil motor. This peculiarity ensures avoiding parasitic vibrations and makes the setup particularly suitable to perform measurements of very low vibration levels. The relative sliding velocity decays along the measurement to zero, which provokes several types of FIV. We employ advanced time-series analysis techniques, such as spectral analysis, attractor reconstruction and recurrence plot analysis to study the dynamical transition from steady sliding to high-frequency FIV and stick-slip vibrations in detail. For different specimens, self-excited vibrations are observed stemming from an instability that is driven by a negative friction-velocity slope characteristic as well as for constant friction values. Prior to instability, it is observed that highly irregular oscillations decay and most of the vibration energy focuses in a low-frequency mode of the experimental setup. The analysis of the FIV range illustrates a plethora of qualitatively different dynamics that can be detected, characterized and visualized using advanced signal processing. Particularly, we report on period-1 and period-2 limit cycles, quasi-periodic motion, weakly chaotic attractors and different types of stick-slip vibrations. The analysis of transitions between those dynamic regimes reveals beating phenomena, sudden energy exchange between different modes and intermittent dynamics. The results of this study aim to provide a step forward on the application of nonlinear dynamics post-processing tools for identifying and characterizing the different frictional stable and unstable scenarios.

Nonlinear Time Series Analysis of Nickel in Sulfuric Acid

Nickel is one of the most important passive metals used in electrodeposition processes in the world. These processes alone consume several million metric tons of nickel yearly. Nickel is well known for its corrosion resistant properties. However, nickel does corrode in H2SO4 and can produce current or potential oscillations in potentiostatic or galvanostatic experiments. Traditional electrochemical studies on Ni oscillating systems are performed by applying applied potential or current during the electrodissolution (corrosion) of single wire electrodes in highly concentrated solutions. External forcing, in which perturbations are applied to systems by an external source, have provided a better understanding of oscillating systems. However, little attention has been given to performing electrochemical studies on electrodeposited metals that produce oscillating systems in lower concentrations of acidic solutions (0.1 M – 1.0 M) and no attention has been given to the possibility for external forcing of these unique systems via concentration change and local heating at the electrode surface until now. The presented work examines the changes in frequency, magnitude, and shape of periodic oscillations and the change in kinetics from temperature changes due to electrical heating and external forcing by independently changing the proton concentration at a nickel electrode. This work improves the understanding of the relationship between periodic oscillation phenomena and the corrosion process of the nickel system in H2SO4.