Narrow Results

Recurrence Plot (RP) and Recurrence Quantification Analysis (RQA) are signal numerical analysis methodologies able to work with nonlinear dynamical systems and nonstationarity. Moreover, they well evidence changes in the states of a dynamical system. We recall their features and give practical recipes. It is shown that RP and RQA detect the critical regime in financial indices (in analogy with phase transition) before a bubble bursts, whence allowing to estimate the bubble initial time. The analysis is made on DAX and NASDAQ daily closing price between January 1998 and November 2003. DAX is studied in order to set-up overall considerations, and as a support for deducing technical rules. The NASDAQ bubble initial time has been estimated to be on 19 October 1999.

We present new measures of complexity and their application to event-related potential data. The new measures are based on structures of recurrence plots and makes the identification of chaos–chaos transitions possible. The application of these measures to data from single-trials of the Oddball experiment can identify laminar states therein. This offers a new way of analyzing event-related activity on a single-trial basis.

Recurrence plots are two-dimensional representations of multidimensional dynamics captured by applying time delays to a single series (vector) of ordinal data in time or space. Recurrence plots may be presented with beautiful lace-like structures, but most important is the inference these patterns make about the underlying dynamics. Complex patterns in recurrence plots can be reduced to primary diagonal, vertical and horizontal dot patterns aligned on a grid. It is the mixing and matching of these primary structures that give rise to all derivative graphical complexities. Once strict definitions are in place, features are easily quantified from recurrence plots of any form including cross recurrence plots.

Although chaotic systems continue to gain interest, their confirmation and analysis can be difficult. Traditional analytic methods impose constraints which are often difficult to achieve. A technique which does not impose these constraints is recurrence quantification analysis. Recurrence quantification is derived from recurrence plots, which are based upon distances matrices of embedded series. The original article demonstrated the plot's ability to uncover deterministic processes, as well as drift and nonstationarity. Recurrence quantification has allowed for direct quantification of these features.

Electrochemical noise (EN) data is commonly used to monitor corrosion of metals in various environments. In this work we use recurrence quantification analysis (RQA) to study EN time series of stainless steel AISI 316 samples immersed in a mildly corrosive electrolyte. It is found that RQA of current and potential time series reveal different information: current time series provides detailed information on the kinetics of the pitting corrosion process, while the potential time series identifies the transitions from one thermodynamic state to another in the pitting corrosion process.

To describe intra-hole fluid convection, fine-scale temperature-time variations were monitored at 25 depth levels within a 50 m long interval (80—130 m depth) in a slim experimental borehole in Sporilov (the Czech Republic). High-resolution temperature data were sampled with a 15 sec time interval for 1.6 up to 2.7 days. The time series obtained were from 10 000 to 16 000 data points. In the upper part of the investigated depth interval, the temperature time series showed a complex oscillation pattern with amplitudes of up to 45 mK (milliKelvin). This variation pattern is alternated with a "quiet" regime below 110 m depth, where temperature oscillations fall within 4–10 mK range.

Convection produced temperature signal was studied by means of recurrence plots and their quantification analysis. This method was proven to be effective to detect transitions in system dynamics. The analysis confirmed a relevant deterministic part in the measured signal (quasi-periodic skeleton) and enabled to quantify the periodic—periodic and periodic—chaotic transitions in the borehole convection dynamics. Thermal dynamics is richer and cooler at shallower depths. The results were confirmed with temperature time series registered at the bottom hole, where the probe penetrated into soft mud debris, which prevented convection, and restricted heat transport to a pure conduction.

We present an analysis of temperature fluctuations in a horizontal round heated turbulent jet. Instantaneous temperature time series were recorded at several points along a horizontal line in the plane of symmetry of the jet. The time series are analyzed using Recurrence Quantification Analysis (RQA). The variation of characteristic RQA measures is associated with and interpreted via the transitions of the physical state of the fluid from the fully-turbulent flow near the jet centerline to the transitional flow near the boundary of the jet.

In ecosystem research, data-driven approaches to modeling are of major importance. Models are more often than not shaped by the spatiotemporal structure of the observations: an inverse modeling approach prevails. Here, I investigate the insights obtained from Recurrence Quantification Analysis of observed ecosystem time series. As a typical example of available long-term monitoring data, I choose time series from hydrology and hydrochemistry. Besides providing insights into the nonstationary and nonlinear dynamics of these variables, RQA also enables a detailed and temporally local model-data comparison.

Identification of disordered regions in protein sequence(s) is a very important problem and a long standing puzzle to biologists. In many proteins, these structural disorders (an outcome of improper protein folding) inside an otherwise ordered structure exhibit many important biological functions. Classical approaches to identify these regions in a sequence rely mainly on the pattern recognition algorithms where amino acid residues are classified as ordered or disordered. In this work, we employ recurrence quantification analysis based approach to understand the complex dynamics underlying these regions. We hypothesize and demonstrate that proteins with disordered regions show a strong evidence of the order-chaos-order transition pattern by using windowed recurrence quantification analysis on a database of 476 proteins available from .

Much evidence suggests complexity in cognitive and motor task performances [Gilden, 2001]. The present study builds upon this work, treating reading of text as a kind of complex coordination or coupling between reader and reading conditions. Three self-paced reading conditions presented connect text in units of different sizes: word, phrase, or sentence units, and repeatedly measure times between spacebar presses to advance the text. The three conditions reveal different patterns across the data. These patterns were evaluated using fractal analyses and Recurrent Quantification Analyses to distinguish highly fluent readers, PhD candidates in English literature, from competent but less fluent undergraduate readers.

Recurrence plots and recurrence quantification analysis have become popular in the last two decades. Recurrence based methods have on the one hand a deep foundation in the theory of dynamical systems and are on the other hand powerful tools for the investigation of a variety of problems. The increasing interest encompasses the growing risk of misuse and uncritical application of these methods. Therefore, we point out potential problems and pitfalls related to different aspects of the application of recurrence plots and recurrence quantification analysis.

A major issue in using recurrence plots (RPs) to study dynamical systems is the choice of neighborhood size for thresholding the distance matrix that creates the plot. This is particularly important for continuous dynamical systems as temporal correlations of the trajectory might provide redundant information for recurrence analysis. We suggest an alternative procedure for creating RPs using the local minima provided by the distance profile, which approximately corresponds to the recurrence information in the orthogonal direction. The local minima-based thresholding yields a clean RP of minimized line thickness, that is compared to the plot obtained by the standard radius bases thresholding. New definitions of line segments arising from the local minima-based method are outlined, which yield consistent results with those derived from standard methods. Our preliminary comparison suggests that the newly introduced thresholding technique is more sensitive to small changes in a system's dynamics. We demonstrate our method via the chaotic Lorenz system without the loss of generality.

The recurrence rate and determinism are two of the basic complexity measures studied in the recurrence quantification analysis. In this paper, the recurrence rate and determinism are expressed in terms of the correlation sum, and strong laws of large numbers are given for them.

Many studies show the possibility of transmitting messages in a protected and covert manner using a noise-like chaotic waveform as a carrier. Among popular chaotic communication system (CCS) types, one may distinguish chaotic shift keying (CSK) and parameter modulation (PM) which are based on the manipulation of the transmitting chaotic oscillators. With the development of direct digital synthesis (DDS), it became possible to modulate chaotic signals by varying the properties of the numerical method used in digital chaos generators. The symmetry coefficient modulation (SCM) is such an approach potentially able to provide higher secrecy. However, the actual security of chaos-based communications is still a questionable and controversial feature. To quantitatively evaluate the CCS security level, a certain numerical metric reflecting the difficulty of breaking a communication channel is needed. Return maps are commonly used to attack chaotic communication systems, but the standard algorithm does not involve any kind of quantification. In this study, we propose a new method for estimating the differences between two return maps based on a two-dimensional (2D) histogram. Then, we investigate the resistance of chaotic shift keying, parameter modulation, and SCM communication schemes against three types of attacks: the proposed quantified return map analysis (QRMA), recurrence quantification analysis (RQA), which had not been previously reported for attacking chaos-based communications, and the classical approach based on spectral analysis. In our experiments we managed to recover the plain binary message from the waveform in the channel when transmitted using all three chaos-based messaging techniques; among them, SCM appeared to be the most secure communication scheme. The proposed QRMA turned out to be the most efficient technique for message recovery: the sensitivity of the QRMA appeared to be 2–5 times higher than that in the case of spectral analysis. The proposed QRMA method can be efficiently used for evaluating the difficulty of hacking chaos-based communication systems. Moreover, it is suitable for the evaluation of any other secure data transmission channel.

The Recurrence Quantification Analysis (RQA), a pattern recognition-based time series analysis method, can be successfully utilized for short, nonstationary, nonlinear, and chaotic time series. These RQA measures quantify several properties of time series, including predictability, regularity, stability, randomness, and complexity. In this regard, first, we analyzed the intraday seasonality with RQA and demonstrated how RQA measures change among the intraday periods by using 160 million row matched orders of 100 shares from Borsa Istanbul Equity Market between 2019M10 and 2020M02. We selected 50 stocks from the BIST50 Index group and 50 stocks from outside of the BIST100 Index group. Since these two share groups exhibit similar intraday RQA seasonality, our results are robust. Second, we explained intraday volatility with RQA measures and found a relationship between RQA measures and intraday volatility using a regression model.

The Sudbury neutrino observatory (SNO) detects ⁸B solar neutrino fluxes from both the D₂O and Salt detector. In the present analysis we have taken into consideration the flux data from 2nd November, 1999 to 27th May, 2001 from the D₂O detector and that from 26th July, 2001 to 28th August, 2003 from the Salt detector. We have applied Delay Vector Variance analysis, 0-1 test, correlation dimension analysis, largest Lyapunov exponent method, recurrence plot and recurrence quantification analysis to explore the complexity and chaosity in these two time series. Present study reveals deterministic chaotic behaviour of these two signals which in turn suggests that long-term forecasting is not possible for these two signals but short-term forecasting can be made provided the model for the process dynamics is known to us.

The nonlinear dynamics of a direct current magnetron sputtering plasma is visualized using recurrence plot (RP) technique. RP comprises the recurrence quantification analysis (RQA) which is an efficient method to observe critical regime transitions in dynamics. Further, RQA provides insight information about the system’s behavior. We observed the floating potential fluctuations of the plasma as a function of discharge voltage by using Langmuir probe. The system exhibits quasi-periodic–chaotic–quasi-periodic–chaotic transitions. These transitions are quantified from determinism, Lmax, and entropy of RQA. Statistical investigations like kurtosis and skewness also studied for these transitions which are in well agreement with RQA results.

Hemiplegia means paralysis of half of the body. It commonly occurs following "stroke", which is due to impedance of blood supply to the brain, hence also termed as "cerebrovascular accident" (CVA). As a consequence of this, the brain tissues suffer from ischemic damage resulting in several symptoms, such as mere weakness, numbness to complete loss of power (paralysis). In order to restore or improve the lost functional movement of the body of the stroke-affected and hemiplegic subjects, a method called functional electrical stimulation (FES) has often been employed as the measure of rehabilitation. FES makes use of low levels of electrical current to activate the nerves and then the muscles, affected. The response of the body to this electrically triggered nervous stimulation could be recorded through different bio-signals. In our work, we measured the accelerometers of hemiplegic patient in two states; with FES and without FES. The nonlinear and nonstationary walking-function-related accelerometers are analyzed using recurrence plots (RP), which helps to visualize the dynamic behavior of the signals. The RPs of electromyography (EMG) signals with stimulation showed distinct periodicity and rhythm when compared to that without stimulation. In addition, we extracted recurrence quantification analysis (RQA) parameters from RP to quantify the obtained information from the RP. Lower values were observed for most of the RQA parameters with FES than obtained without FES. This also confirmed the fact that FES is very useful in bringing more order, rhythm and better control in the physical activities of hemiplegic people.

Epilepsy is a common neurological disorder characterized by recurrence seizures. Alcoholism causes organic changes in the brain, resulting in seizure attacks similar to epileptic fits. Hence, it is challenging to differentiate the cause of fits as epileptic or alcoholism, which is important for deciding on the treatment in the neurology ward. The focus of this paper is to automatically differentiate epileptic, normal, and alcoholic electroencephalogram (EEG) signals. As the EEG signals are non-linear and dynamic in nature, it is difficult to tell the subtle changes in these signals with the help of linear techniques or by the naked eye. Therefore, to analyze the normal (control), epileptic, and alcoholic EEG signals, two non-linear methods, such as recurrence plots (RPs) and then recurrence quantification analysis (RQA) are adopted. Approximately 10 RQA parameters have been used to classify the EEG signals into three distinct classes, i.e., normal, epileptic, and alcoholic. Six classifiers, such as support vector machine (SVM), radial basis probabilistic neural network (RBPNN), decision tree (DT), Gaussian mixture model (GMM), k-nearest neighbor (kNN), and fuzzy Sugeno classifiers have been developed to accomplish this task. Results show that the GMM classifier outperformed the other classifiers with a classification sensitivity of 99.6%, specificity of 98.3%, and accuracy of 98.6%.

Characterizing the brain activity during anesthesia is considered a major challenge for researchers. The concentration-relevant effect of the sevoflurane is evaluated on EEG signals collected from 19 patients during a proscribed induction and recovery setup. Recurrence Quantification Analysis based on order patterns is employed to provide an index named order laminarity (OLAM) to evaluate changes in the neuronal system. This index computes the activity of a part of brain without considering the number or dynamical nature of the individual sources and signifies segments staying in the same phase space region for a short time. Pharmacokinetic-pharmacodynamic modeling and statistical features are used to assess the effectiveness of the OLAM index compared with response entropy index as implemented in the commercial Datex-Ohmeda Module. Both methods track the overall changes in EEG. However, the OLAM can be proficiently computed and is artifact resistant (standard deviation of 0.016 for OLAM relative to 0.02 for response entropy index). This measure as a neurophysiologic correlation of general anesthesia also reacts quicker to alternations in EEG signals during induction and correlates more powerfully with drug concentration (The prediction probability of 0.89 for OLAM is proportionate to 0.83 for response entropy). This examination exemplifies a crucial translational phase from the neuroscience of consciousness to more intricate monitoring of anesthetic effects in patients.