Time and Again:

The methods of recurrence plots (RPs) and recurrence quantification analysis (RQA) have been used to investigate the tribosystem. The morphology of RPs and RQA measures are strongly dependent on the embedding parameters of the recursive matrix and the segment sizes of the time-series. To improve the calculation accuracy of recursive characteristics analysis, the influences of the embedding parameters and segment sizes on the morphology of RPs and RQA measures have been studied in this letter. Three kinds of theoretical chaotic time-series and measured coefficient of friction (COF) signals during the running-in process were chosen as research objects, and the morphology of RPs and RQA measures were obtained using CRP toolbox afterward. The results indicate that no embedding was actually needed if the data sets are to be qualitatively analyzed using RPs and RQA. Additionally, the morphology of RPs and RQA measures are sensitive to the segment sizes for theoretical chaotic time-series, while the RQA measures of COF signal in the steady-state period are rather stable due to its self-similarity. Finally, according to the guidelines of the parameter settings, the dynamical evolution of measured COF signals during the running-in process have been investigated. It is indicated that recursive characteristics of COF signals could reveal the tribological behaviors’ evolution and conduct the running-in status identification. The results in this paper are significant for improving the calculation accuracy and saving computational time when using the method of recursive characteristics analysis on the tribological behaviors.

In the paper, application of the Recurrence Plots (RP) method to damage detection and localization in the beam structure is proposed. The RP is a well-established method of nonlinear data analysis dedicated to investigation into changes in dynamic behaviour of mechanical systems during their normal work. Interpretation of information provided by the recurrence plots can be supported by the estimation of the measures of Recurrence Quantification Analysis (RQA).

Recurrence quantification analysis (RQA) is a time-series analysis method that uses autocorrelation properties of typing data to detect regularities within the writing process. The following paper first gives a detailed introduction to RQA and its application to time series data. We then apply RQA to keystroke logging data of first and foreign language writing to illustrate how outcome measures of RQA can be understood as skill-driven constraints on keyboard typing performance. Forty native German students performed two prompted writing assignments, one in German and one in English, a standardized copy task, and a standardized English placement test. We assumed more fluent and skilled writing to reveal more structured typing time series patterns. Accordingly, we expected writing in a well-mastered first language to coincide with higher values in relevant RQA measures as compared to writing in a foreign language. Results of mixed model ANOVAs confirmed our hypothesis. We further observed that RQA measures tend to be higher, thus indicating more structured data, whenever parameters of pause, burst, and revision analyses indicate more fluent writing. Multiple regression analyses revealed that, in addition to typing skills, language proficiency significantly predicts outcomes of RQA. Thus, the present data emphasize RQA being a valuable resource for studying time series data that yields meaningful information about the effort a writer must exert during text production.

<p>Grassland ecosystems are extremely complex and set up intricate structures, whose characteristics and dynamic properties are greatly influenced by climate and meteorological patterns. Climate change and global warming are factors that could impact negatively in the quality and productivity of these ecosystems.</p><p>Remote sensing techniques have been demonstrated as a powerful tool for monitoring extensive areas. In this study, two semi-arid grassland plots were selected in the centre of Spain. This region is characterized by low precipitation and moderate productivity per unit. Through scientific research, spectral vegetation indices (VIs) have been developed to characterize vegetation cover. The most common VI is the Normalized Difference Vegetation Index (NDVI). However, in vegetation scarcity conditions, bare soil reflectance is increased, and the feasibility of NDVI is reduced. This study aims to perform a method to compare soil and agro-climatic variables effect on vegetation time-series indices.</p><p>The construction of the time series was based on multispectral images of MODIS TERRA (MOD09A1.006) product acquired from 2002 till 2018. Three pixels with a temporal resolution of 8 days and a spatial resolution of 500 x 500 m were chosen in each area. To estimate and analyse VIs series, Red (620-670 nm) and Near Infrared (841-876 nm) channels were extracted and filtered by the quality of pixel. All spectral bands showed statistically significant differences confirming that both areas presented different soil properties. Moreover, average annual precipitation was different in each area of study.</p><p>NDVI calculation is only based on NIR and RED bands. To improve the estimation of vegetation in semi-arid areas, several indices have been developed to minimize the soil effect. Each one of them incorporates soil influence in a different way, i.e., Soil Adjusted Vegetation Index (SAVI) adds a constant soil adjustment factor (L), whereas, MSAVI, incorporate an L variable and dependant on soil characteristics.</p><p>Recurrence plots (RP) and recurrence quantification analysis (RQA) were computed to characterize the influence of agro-climatic variables in vegetation index dynamics. Characterization was based on various RQA measures, such as Determinism (DET), average diagonal length (LT) or entropy (ENT).</p><p>Our results showed different RPs depending on the area, VI utilized and precipitation. MSAVI patterns were further distinct, meanwhile, NDVI showed a noisy pattern. LT values in MSAVI were higher than in SAVI implying that MSAVI recurrent events are much longer than SAVI. Simultaneously, LT and DET values in ZSO, with a higher rain, were above ZEA values in MSAVI.</p><p>This indicates that incorporating more detailed information of soil and precipitation reinforce vegetation index estimation and allow to obtain a more distinct pattern of the time series. Therefore, in arid-semiarid grasslands, they should be considered.</p><p><strong>ACKNOWLEDGEMENTS</strong></p><p>The authors acknowledge support from Project No. PGC2018-093854-B-I00 of the Spanish <em>Ministerio de Ciencia Innovación y Universidades</em> of Spain and the funding from the Comunidad de Madrid (Spain) and Structural Funds 2014-2020 512 (ERDF and ESF), through project AGRISOST-CM S2018/BAA-4330, are highly appreciated.</p>

This paper presents efficient low-power adaptive filter architecture for electroencephalogram (EEG) signal and epileptic seizure detection using recurrence quantification analysis (RQA). The preprocessing of EEG is done using notch, wavelet and adaptive filter. The comparison of signal-to-noise ratio of the filter outputs proves that the adaptive filter provides better performance and a parallel interleaved sample of direct form adaptive FIR filter architecture is implemented and low-power issues are addressed. An innovative compressor-based addition technique is utilized in the filter implementation to reduce the area and power consumption. The design is developed using Verilog HDL and mapped to 65-nm technological node. The power results are compared with conventional architecture of adaptive filter. The major advantage of choosing RQA is that it provides better information even for short non-stationary and nonlinear signals where other methods fail to provide good results. And it requires no conventions about data set size or dispersal of the data. The algorithm is applied on epileptic EEG signal from CHB-MIT database. The RQA measures are determined from the recurrence plot, its performance is measured in terms of sensitivity and specificity as 97.4 and 93.5 %, respectively, and leakage power is reduced to 10 %.

The recurrence plot and the recurrence quantification analysis (RQA) are well-established methods for the analysis of data from complex systems. They provide important insights into the nature of the dynamics, periodicity, regime changes, and many more. These methods are used in different fields of research, such as finance, engineering, life, and earth science. To use them, the data have usually to be uniformly sampled, posing difficulties in investigations that provide non-uniformly sampled data, as typical in medical data (e.g., heart-beat based measurements), paleoclimate archives (such as sediment cores or stalagmites), or astrophysics (supernova or pulsar observations). One frequently used solution is interpolation to generate uniform time series. However, this preprocessing step can introduce bias to the RQA measures, particularly those that rely on the diagonal or vertical line structure in the recurrence plot. Using prototypical model systems, we systematically analyze differences in the RQA measure average diagonal line length for data with different sampling and interpolation. For real data, we show that the course of this measure strongly depends on the choice of the sampling rate for interpolation. Furthermore, we suggest a correction scheme, which is capable of correcting the bias introduced by the prepossessing step if the interpolation ratio is an integer.

In this study, we present results of the application of nonlinear time series analysis on traffic data for incident detection. More specifically, we analyze daily volume records of Attica Tollway (Greece) collected from sensors located at various locations. The analysis was performed using the Recurrence Plot (RP) and Recurrence Quantification Analysis (RQA) method of the volume data of the lane closest to the median. The results show that it is possible to identify, through the abrupt change of the dynamics of the system revealed by RPs and RQA, the occurrence of incidents on the freeway and differentiate from recurrent traffic congestion. The proposed methodology could be of interest for big data traffic analysis.

Purpose: To investigate if there exists a difference in breathing patterns between patients treated with SBRT and IMRT using RQA and DC (using K2: correlation entropy and D2: correlation dimension) measures. Methods: 9 patients treated with SBRT and 8 treated with IMRT were scanned with 4D CT and the breathing patterns were acquired. One of the SBRT patients was scanned with and without meditation. Each breathing signal consisted of a scalar time series and recurrence quantification analysis (RQA) was utilized to determine the following measures: Periodicity of the system as percentage of recurrence points (%RR), determinism (DET), maximum diagonal line length (L_max) whose inverse the divergence (DIV) is measure for how fast trajectories diverge from each other, the average diagonal line length (L) that can be interpreted as the mean prediction time of the signal, and the entropy (ENTR) a measure of information complexity. In addition the invariant measures of K2 and D2 were also estimated. A locally nonlinear forecast was applied to predict future breathing signals of N time step ahead for the patient with and without meditation. Results: Our results showed %RR has significant correlation with L_max and has inverse correlation with DIV. DET has significant correlation with Lmax, L, ENTR and DIV. Independent t test suggests there is no difference between the SBRT and IMRT groups in terms of the RQA measures and K2. Patient that had undergone meditation showed improvement in %RR, L_max, DIV, K2 and had an estimated correlation dimension of 1.7. Prediction showed similar results for one and three time step ahead but meditation one had better prediction horizon when time step was higher. Conclusion: RQA is a powerful tool that allows one to analyze the dynamic nature of breathing pattern. No significant difference was found in the dynamical complexity of SBRT and IMRT patients.

The purpose of this study was to apply recurrence plots and recurrence quantification analysis (RQA) on event related potentials (ERPs) recorded during memory recognition tests. Data recorded during memory retrieval in four scalp region was used. Tow most important ERP's components corresponding to memory retrieval, FN400 and LPC, were detected in recurrence plots computed for single-trial EEGs. In addition, the RQA was used to quantify changes in signal dynamic structure during memory retrieval, and measures of complexity as RQA variables were computed. Given the stimulus, amplitude of the RQA variables increases around 400ms, corresponding to dimension reduction of system. Furthermore, after 800ms these amplitudes decreased which can be as a consequence of an increase in system dimension and back to its basic state. The mean amplitude of Old items was more than New one. Using this method, we found its ability to detect memory components of EEG signals and do a distinction between Old/ New items. In contrast with linear techniques recurrence plots and RQA do not need large number of recorded trials, and they can indicate changes in even single-trial EEGs. RQA can also show differences between old and new events in a memory process.

In this paper the dynamical properties of ARP data for anomaly of internet traffic detection are presented. The local network traffic dynamics for single workstation has been observed experimentally on networks with 42 workstations. In the paper RQA (Recurrence Quantification Analysis) measures have been analyzed. Three of them have been explored using RP windowing method: recurrence rate (RR), divergence (DIV) and the longest vertical line (VMAX). The RP windowing algorithm samples the explored ARP time series, as a result each RP window characterized the disintegration of recurrence plots. The RR and VMAX defined the low activity of ARP dataflow. Inversely, the DIV identified the high activity of ARP time series. The authors have proved that both, the recurrence plot technique and the RP windowing method as the tools in the analysis of network traffic anomaly detection are effective and accurate.

Our contribution focuses on the characterization of sleep apnea from a cardiac rate point of view, using Recurrence Quantification Analysis (RQA), based on a Heart Rate Variability (HRV) feature selection process. Three parameters are crucial in RQA: those related to the embedding process (dimension and delay) and the threshold distance. There are no overall accepted parameters for the study of HRV using RQA in sleep apnea. We focus on finding an overall acceptable combination, sweeping a range of values for each of them simultaneously. Together with the commonly used RQA measures, we include features related to recurrence times, and features originating in the complex network theory. To the best of our knowledge, no author has used them all for sleep apnea previously. The best performing feature subset is entered into a Linear Discriminant classifier. The best results in the “Apnea-ECG Physionet database” and the “HuGCDN2014 database” are, according to the area under the receiver operating characteristic curve, 0.93 (Accuracy: 86.33%) and 0.86 (Accuracy: 84.18%), respectively. Our system outperforms, using a relatively small set of features, previously existing studies in the context of sleep apnea. We conclude that working with dimensions around 7–8 and delays about 4–5, and using for the threshold distance the Fixed Amount of Nearest Neighbours (FAN) method with 5% of neighbours, yield the best results. Therefore, we would recommend these reference values for future work when applying RQA to the analysis of HRV in sleep apnea. We also conclude that, together with the commonly used vertical and diagonal RQA measures, there are newly used features that contribute valuable information for apnea minutes discrimination. Therefore, they are especially interesting for characterization purposes. Using two different databases supports that the conclusions reached are potentially generalizable, and are not limited by database variability.

Detecting intrinsic dynamics of traffic flow with recurrence analysis and empirical mode decomposition

<p>Clouds are the source of the biggest uncertainty in weather and climate models. One cannot fully understand clouds without understanding turbulence and microphysical processes in clouds. EUREC4A [1] experiment conducted during January and February focused on studying stratocumulus clouds (the most common marine clouds on earth) in atmoshperic boundary layer near Barbados. One of many measurements conducted during the campaign, was one using Twin-Otter aircraft, on which an Ultra Fast Thermometer 2b [2] was mounted. This thermometer, developed at Institute of Geophysics at the University of Warsaw is able to measure temperature at a 20 kHz frequency. After averaging to a frequency of 2 kHz, and assuming that the plane is moving at an average speed of 60 m/s, the spatial resolution of the thermometer is of the order of centimeters. The aircraft performed cloud penetrations together with measurements of temperature and other parameters such as the three components of wind velocity, pressure and humidity. The proposed method to study temperature time series is the time-dependent Recurrence Quantification Analysis (RQA) [3].</p><p>Recurrence Plots (RPs) are a visualization of a square matrix, which elements correspond to the moments when the system recurs, or when phase space trajectory of a system visits the same area in the phase space. RQA is a technique of data analysis based on the analysis of structures present in RPs. This method is used to study non-linear behaviors in the system, and to study determinism and chaos of the system, and transitions between them. In this study, portions of temperature records corresponding to cloud penetration were analyzed.</p><p>The analyzed clouds were divided into groups based on the angle of the penetration (windward, leeward, or from the side), as well as the variability of the wind during the penetration. Preliminary results suggest that the sharp edges of either the windward side of a dissipative cloud or both sides of a developing cloud are the places where the behavior of temperature is the most stochastic. Some clouds exhibited a behavior where the temperature behavior shifted from more stochastic near the windward side to more deterministic near the leeward side of the cloud. There are also side penetrations that, based on the RQA, contain information about the structure of the cloud and its dynamical properties.</p><p>We acknowledge funding by Poland’s National Science Centre grant no. UMO-2018/30/M/ST10/00674.</p><p>[1] Stevens B. et. al. 2021: EUREC4A, Earth System Science Data, vol. 13(8), pp. 4067-4119, 10.5194/essd-13-4067-2021<br>[2] Kumala, W. et. al. 2013: Modified ultrafast thermometer UFT-M and temperature measurements during Physics of Stratocumulus Top (POST), Atmos. Meas. Tech., vol. 6, pp. 2043–2054, 10.5194/amt-6-2043-2013<br>[3] N. Marwan, et. al. 2007: Recurrence Plots for the Analysis of Complex Systems, Physics Reports, vol. 438(5–6), pp. 237–329, 10.1016/j.physrep.2006.11.001</p>

We present an approach to recurrence quantification analysis (RQA) that allows to process very long time series fast. To do so, it utilizes the paradigm Divide and Recombine. We divide the underlying matrix of a recurrence plot (RP) into sub matrices. The processing of the sub matrices is distributed across multiple graphics processing unit (GPU) devices. GPU devices perform RQA computations very fast since they match the problem very well. The individual results of the sub matrices are recombined into a global RQA solution. To address the specific challenges of subdividing the recurrence matrix, we introduce means of synchronization as well as additional data structures. Outperforming existing implementations dramatically, our GPU implementation of RQA processes time series consisting of $$N\approx $$ 1,000,000 data points in about 5 min.

The movement of lifting heavy objects with upper limb exoskeleton is a dynamic process of multi-muscle coordination. Muscle fatigue occurs after repetitive lifting heavy objects with exoskeleton robot for a long time. Due to the dynamic characteristics of the moving process, the traditional linear analysis methods can not fully characterize the muscle fatigue problem of upper limb. In this paper, a novel approach base on ross recurrence plot (CRP)and recurrence quantification analysis (RQA)is proposed to analyze the progression of muscle fatigue of upper limb. Firstly, distance threshold and date length of the recurrence plot is chosen according to the RP dynamical structures of the electromyography (EMG)signals. Then the phase space reconstruction techniques and recurrence plot theory are utilized to analyze the nonstationarity characteristics of the multichannel and single-channel surface EMG signals during the fatigue process. Finally, the RQA indices of the overall and local muscles are calculated. The experiments show that the CRP can qualitatively reflect the change of muscle fatigue state. Meanwhile, the RQA indices of multi-channel and single-channel EMG signals can quantitatively reveal the changes of muscle fatigue from the overall and local perspectives. This method provides a theoretical basis for evaluating muscle fatigue during repeated moving in the way of nonlinear dynamics.