Recurrence Quantification Analysis Research Articles

Unveiling emotion dynamics in problem-solving: a comprehensive analysis with an intelligent tutoring system using facial expressions and electrodermal activities

Emotions play a crucial role in the learning process, yet there is a scarcity of studies examining emotion dynamics in problem-solving with fine-grained data and advanced tools. This study addresses this gap by investigating the emotional trajectories during self-regulated learning (SRL) phases (i.e., forethought, performance, and self-reflection) among 47 medical students utilizing an intelligent tutoring system. Real-time facial expressions were analyzed through recurrence quantification analysis alongside an examination of electrodermal activities (EDA) across the SRL phases. The findings reveal that emotion stability varied across SRL phases, with students exhibiting more stable emotions during the performance phase. Compared to the forethought and self-reflection phases, students had less frequent and lower intensity of emotional arousal in the performance phase. Moreover, we found that students with better performance demonstrated more stable emotions in the forethought phase, less stable emotions in the self-reflection phase, and a higher level of emotional arousal in the self-reflection phase. These insights highlight the temporal and dynamic nature of emotions in SRL, offering methodological and educational implications for leveraging facial expressions and EDA to monitor and enhance students’ emotional experience during problem-solving.

Characterization of heart rate variability in end-stage renal disease patients after kidney transplantation with recurrence quantification analysis.

Heart rate variability (HRV) is a noninvasive approach to studying the autonomic modulation of heart rate in experimental settings, such as active standing sympathetic stimulation. It is known that patients with end-stage renal disease during active standing have few changes in HRV dynamics, which are improved after hemodialysis. However, it is unknown whether the response to active standing is recovered after definitive treatment with kidney transplantation. This work aims to assess the change in HRV dynamics in the supine position and active standing through time and frequency-based metrics, as well as recurrence plot quantitative analysis (RQA). We studied HRV dynamics by obtaining 5-minute electrocardiographic recordings from kidney transplant recipients who underwent an active standing test. The mean duration of heartbeats and their standard deviation diminished in active standing, compared with the supine position. Also, the low-frequency component of HRV and the presence of diagonal and vertical structures in RQA were predominant. A larger estimated glomerular filtration rate was significantly correlated with broader HRV in the supine position and during active standing. The narrower HRV during active standing may indicate a sympathetic response to external stimuli, which is expected in a functional cardiovascular system, and may be influenced by renal function.

Electromagnetic field and chaotic charged-particle motion around hairy black holes in Horndeski gravity

The Wald vector potential is an exact solution of the source-less Maxwell equations regarding an electromagnetic field of a vacuum uncharged black hole like the Kerr background black hole in an asymptotically uniform magnetic field. However, it is not if the black hole is a nonvacuum solution in a theory of modified gravity with extra fields or a charged Kerr–Newman spacetime. To satisfy the source-less Maxwell equations in this case, the Wald vector potential must be modified and generalized appropriately. Following this idea, we derive an expression for the vector potential of an electromagnetic field surrounding a hairy black hole in the Horndeski modified gravity theory. Explicit symplectic integrators with excellent long-term behaviour are used to simulate the motion of charged particles around the hairy black hole immersed in the external magnetic field. The recurrence plot method based on the recurrence quantification analysis uses diagonal structures parallel to the main diagonal to show regular dynamics, but adopts no diagonal structures to indicate chaotic dynamics. The method is efficient to detect chaos from order in the curved spacetime, as the Poincaré map and the fast Lyapunov indicator are.

Personality expression in body motion dynamics: An enactive, embodied, and complex systems perspective

We studied body motion dynamics and personality differences using complex systems methods. 105 adults (aged 18–33, 70% women) completed a 15-minute laboratory task covering three self-referencing topics (self-introduction, bodily perception/sensory life, socio-emotional life). Body motion dynamics were extracted from videos using a frame-by-frame differentiation method. Recurrence Quantification Analysis derived the measures of Determinism, Entropy, Laminarity, and Mean-Line. Multilevel models estimated personality (IPIP-NEO-120) and situational effects. Neuroticism predicted lower determinism and fluctuating dynamics in bodily perception and socioemotional life; less complexity and stability during socioemotional topics, and increased negative affect. Extraversion predicted regular/deterministic dynamics during bodily perception. Conscientiousness predicted lower determinism and increased variability. Agreeableness predicted lower post-task negative affect. Findings are discussed within embodied, enactive, complex systems, and personality frameworks.

A GRU–CNN model for auditory attention detection using microstate and recurrence quantification analysis

Attention as a cognition ability plays a crucial role in perception which helps humans to concentrate on specific objects of the environment while discarding others. In this paper, auditory attention detection (AAD) is investigated using different dynamic features extracted from multichannel electroencephalography (EEG) signals when listeners attend to a target speaker in the presence of a competing talker. To this aim, microstate and recurrence quantification analysis are utilized to extract different types of features that reflect changes in the brain state during cognitive tasks. Then, an optimized feature set is determined by employing the processes of significant feature selection based on classification performance. The classifier model is developed by hybrid sequential learning that employs Gated Recurrent Units (GRU) and Convolutional Neural Network (CNN) into a unified framework for accurate attention detection. The proposed AAD method shows that the selected feature set achieves the most discriminative features for the classification process. Also, it yields the best performance as compared with state-of-the-art AAD approaches from the literature in terms of various measures. The current study is the first to validate the use of microstate and recurrence quantification parameters to differentiate auditory attention using reinforcement learning without access to stimuli.

Routineness of Social Interactions Is Associated With Higher Affective Well-Being in Older Adults.

Some research conceptualizes routineness of daily life as an indicator of cognitive vulnerability that would lead to lower well-being in older age, whereas other research expects routineness to give rise to more meaning and stability in life and thus to higher well-being. Further research is needed to understand routineness in older adults in relation to cognitive abilities and well-being. This study examined routineness of social interactions. We examined data from an event-contingent experience sampling study with 103 Swiss community-dwelling older adults (aged 65 to 84 years). Participants completed in-lab cognitive assessments (reasoning, episodic memory, speed, and vocabulary) and reported their well-being (positive affect, negative affect, and life satisfaction). For more than 21 days, participants reported the time and context of their social interactions (including modality, partner type, and location). Routineness of social interactions was defined as social interactions that occurred at the same time of day over the study period. It was calculated using recurrence quantification analysis. Linear regressions showed that higher routineness of social interaction in general, of social interaction through the same modality, and of social interaction with the same partner type were associated with higher positive affect. Higher routineness of social interaction in general was associated with lower negative affect. Routineness of social interactions was not associated with life satisfaction or cognitive abilities. A routine social life may increase older adults' affective well-being. Results are discussed in the context of activity engagement and time use in older age.

The effects of Tai Chi on standing balance control in older adults may be attributed to the improvement of sensory reweighting and complexity rather than reduced sway velocity or amplitude.

Tai Chi has proved to be an effective therapy for balance performance and cognition. However, non-consistency exists in the results of the effect of Tai Chi training on standing balance control in older adults. This study aimed to use traditional and non-traditional methods to investigate the effect of Tai Chi on standing balance in older adults. Thirty-six Tai Chi practitioners (TC group) and thirty-six older adults with no Tai Chi practice (control group) were recruited in this study. A Nintendo Wii Balance Board was used to record the center of pressure (COP) during standing balance over 20 s in the condition of eyes closed with three repetitions. The wavelet analysis, multiscale entropy, recurrence quantification analysis, and traditional methods were used to evaluate the standing balance control in the anterior-posterior (AP) and mediolateral (ML) directions. (1) Greater sway mean velocity in the AP direction and sway Path length were found in the TC group compared with the control group; (2) lower Very-low frequency band (0.10-0.39 Hz) and higher Moderate frequency band (1.56-6.25 Hz) in the AP and ML directions were found in the TC group compared with the control group; (3) greater complexity index (CI) and lower determinism (DET) in the AP and ML directions were observed in the TC group compared with control group; (4) greater path length linked with smaller Very-low frequency band in the AP and ML directions and higher Moderate frequency band in the AP direction in both groups; (5) greater path length linked with lower DET and higher CI in the AP direction only in the TC group. Long-term Tai Chi practice improved sensory reweighting (more reliance on the proprioception system and less reliance on the vestibular system) and complexity of standing balance control in older adults. In addition, greater sway velocity may be as an exploratory role in standing balance control of TC older adults, which correlated with greater complexity, but no such significant relationship in the control group. Therefore, the effects of Tai Chi practice on standing balance control in older adults may be attributed to the improvement of sensory reweighting and complexity rather than reduced sway velocity or amplitude.

The credit card-augmented Divisia monetary aggregates: an analysis based on recurrence plots and visual boundary recurrence plots

In this paper, we compare the dynamics of the growth rates of the original Divisia monetary aggregates, the credit card-augmented Divisia monetary aggregates, and the credit card-augmented Divisia inside monetary aggregates. This analysis is based on the methods of recurrence plots, recurrence quantification analysis, and visual boundary recurrence plots which are phase space methods designed to depict the underlying dynamics of the system under study. We identify the events that affected Divisia money growth and point out the differences among the different Divisia monetary aggregates based on the recurrence and visual boundary recurrence plots. We argue that the broad Divisia monetary aggregates could be used for monetary policy and business cycle analysis as they are exhibiting less fluctuation compared to the narrow Divisia monetary aggregates. They could positively affect policy decisions regarding environmental choices and sustainability. We also point out the changes in the monetary dynamics locating the 2008 global financial crisis and the Covid-19 pandemic.

Synchrophasor-Based Real-Time Detection for Power System Events With Fast and Slow Dynamics via Dual Windowed Recurrence Quantification Analysis Algorithm

Synchrophasor-Based Real-Time Detection for Power System Events With Fast and Slow Dynamics via Dual Windowed Recurrence Quantification Analysis Algorithm

An alternative EMG normalization method: Heterogeneous recurrence quantification analysis of isometric maximum voluntary contraction movements

This study presents an alternative method of normalizing Surface Electromyography (EMG) signals, which provide valuable insights into the musculoskeletal properties of the human body. Traditional normalization through the peak maximum voluntary contraction (MVC) method may result in variable outcomes due to its dependence on pre-processing steps such as smoothing and window length. To address this issue, the study standardizes the EMG pre-processing steps by using non-linear techniques, namely recurrence quantification analysis (RQA) and heterogeneous RQA (HRQA). RQA, specifically HRQA, functions as EMG feature extractors to explore the nonlinear dynamical system and state space trajectories of chaotic EMG signals. Principal component analysis (PCA) and kernel PCA (KPCA) were further applied to the RQA and HRQA results to obtain data with more information. The results show that the first principal components (PC1 and KPC1) of HRQA have a very strong relationship with peak MVC (ρ > |0.90|, p < 0.001), indicating their potential compared to the traditional EMG normalization technique for lower limb muscle groups. Additionally, the study investigated the dynamic differences among isometric MVC movements in lower limb muscle groups and found that the RQA and HRQA methods indicated a greater separation for detecting these differences compared to peak MVC. This study offers a valuable method for assessing the musculoskeletal characteristics of individuals who may have difficulty with activities like walking or providing maximum force during EMG data collection, such as those suffering from Parkinson's disease or walking disabilities. This enhances our understanding of their musculoskeletal properties.

Can Recurrence Quantification Analysis Be Useful in the Interpretation of Airborne Turbulence Measurements?

AbstractIn airborne data or model outputs, clouds are often defined using information about Liquid Water Content (LWC). Unfortunately LWC is not enough to retrieve information about the dynamical boundary of the cloud, that is, volume of turbulent air around the cloud. In this work, we propose an algorithmic approach to this problem based on a method used in time series analysis of dynamical systems, namely Recurrence Plot (RP) and Recurrence Quantification Analysis (RQA). We construct RPs using time series of turbulence kinetic energy, vertical velocity and temperature fluctuations as variables important for cloud dynamics. Then, by studying time series of laminarity (LAM), a variable which is calculated using RPs, we distinguish between turbulent and non‐turbulent segments along a horizontal flight leg. By selecting a single threshold of this quantity, we are able to reduce the number of subjective variables and their thresholds used in the definition of the dynamical cloud boundary.

Non-destructive characterization of dislocation density in annealed pure iron using nonlinear ultrasonic combined with recurrence quantification analysis

Non-destructive characterization of dislocation density in annealed pure iron using nonlinear ultrasonic combined with recurrence quantification analysis

A rolling bearing fault diagnosis technique based on recurrence quantification analysis and Bayesian optimization SVM

A rolling bearing fault diagnosis technique is proposed based on Recurrence Quantification Analysis (abbreviated as RQA) and Bayesian optimized Support Vector Machine (abbreviated as RQA-Bayes-SVM). Firstly, analyzing the vibration signal with recurrence plot and the nonlinear feature parameters are extracted with RQA, constructing a feature matrix describing the fault mode and fault degree comprehensively. Finally, Bayesian optimization algorithm is introduced for searching the best penalty factor C and kernel function parameter g of SVM and establishing an optimal Bayes-SVM model. Bearing datasets from CWRU is imported for diagnosis on fault mode and fault degree. The results show that the technique presents a good performance on fault mode diagnosis as well as fault degree distinction. Compared with common k-Nearest Neighbor (abbreviated as KNN) and Random Forest (abbreviated as RF) diagnosis models, Bayes-SVM has the best accuracy and stability, which indicates a potential value for engineering applications.

A novel bionic olfactory network combined with an electronic nose for identification of industrial exhaust

Traditional electronic nose (E-nose) signal processing methods and classification techniques are often cumbersome, heavily dependent on the experience of the implementers and poor in biological interpretability. In view of the above problems, a novel bionic olfactory network is proposed for processing E-nose data for industrial exhaust identification. First, the bionic olfactory network (BON) consists of a bionic olfactory bulb system (BOBS) and a bionic olfactory cortex (BOC). The BOBS highly simulates the odor information conduction function of the mammalian olfactory bulb and is composed of a novel bionic olfactory bulb model and recurrence quantification analysis (RQA), which can transform the original sensor responses into neuron spike sequences and extract features from the sequences, simplifying traditional data processing steps. The BOC is a convolutional spiking neural network that primarily imitates the odor information recognition function of the olfactory cortex in the mammalian olfactory system. The whole BON exhibits excellent biological interpretability due to its unique mode of information transmission. Finally, the experimental data of ten types of industrial exhaust were collected by using a self-built E-nose system. The experimental results indicate that the classification accuracy of the BON is 94.4%, which is much better than that of the combination of traditional signal processing methods and classification techniques. An even better recognition accuracy of 79.2% can be obtained in small sample training, which is still the best performance.

Vectorgastrogram: dynamic trajectory and recurrence quantification analysis to assess slow wave vector movement in healthy subjects.

Functional gastric disorders entail chronic or recurrent symptoms, high prevalence and a significant financial burden. These disorders do not always involve structural abnormalities and since they cannot be diagnosed by routine procedures, electrogastrography (EGG) has been proposed as a diagnostic alternative. However, the method still has not been transferred to clinical practice due to the difficulty of identifying gastric activity because of the low-frequency interference caused by skin-electrode contact potential in obtaining spatiotemporal information by simple procedures. This work attempted to robustly identify the gastric slow wave (SW) main components by applying multivariate variational mode decomposition (MVMD) to the multichannel EGG. Another aim was to obtain the 2D SW vectorgastrogram VGGSW from 4 electrodes perpendicularly arranged in a T-shape and analyse its dynamic trajectory and recurrence quantification (RQA) to assess slow wave vector movement in healthy subjects. The results revealed that MVMD can reliably identify the gastric SW, with detection rates over 91% in fasting postprandial subjects and a frequency instability of less than 5.3%, statistically increasing its amplitude and frequency after ingestion. The VGGSW dynamic trajectory showed a statistically higher predominance of vertical displacement after ingestion. RQA metrics (recurrence ratio, average length, entropy, and trapping time) showed a postprandial statistical increase, suggesting that gastric SW became more intense and coordinated with a less complex VGGSW and higher periodicity. The results support the VGGSW as a simple technique that can provide relevant information on the "global" spatial pattern of gastric slow wave propagation that could help diagnose gastric pathologies.

Analytical results in calculating the entropy of recurrence microstates

Since the development of recurrence plots (RP) and recurrence quantification analysis (RQA), there has been a growing interest in many areas in studying physical systems using recursion techniques. In particular, as part of the RQAs, we observed the development of the concept of recurrence microstates, defined as small blocks obtained from a recurrence graph. It can be shown that some other RQAs can be calculated as a function of recurrence microstates, and the probabilities of occurrences of these microstates can define an information entropy, the so-called entropy of recurrence microstates. It was also observed that recurrence microstates and recurrence entropy can distinguish between correlated and uncorrelated stochastic and deterministic states, due to their symmetry properties. In this paper we propose analytical expressions for calculating the entropy of recurrence microstates, avoiding the need to sample a large set of recurrence microstates. The results can be particularly important in quantifying small amounts of data, where significant sampling of microstates may not be possible. In this paper we propose analytical expressions to compute the entropy of recurrence microstates avoiding the need to sample a large set of recurrence microstates. We show that our results are accurate for cases where the probability distribution function is known. For other situations, the results can be calculated approximately. Another important fact is that the approximate results can be generalized to any size of microstate, making them a powerful tool for calculating the entropy of recurrence. Our approximate methods allow us to know what these properties are and how to exploit this quantifier in the best possible way, with minimal memory usage. Finally, we show that our analytical results are in remarkable agreement with numerical simulations.

Monitoring of Thermoacoustic Combustion Instability via Recurrence Quantification Analysis and Optimized Deep Belief Network

Thermoacoustic oscillation is indeed a phenomenon characterized by the symmetric coupling of thermal and acoustic waves. This paper introduces a novel approach for monitoring and predicting thermoacoustic combustion instability using a combination of recurrence quantification analysis (RQA) and an optimized deep belief network (DBN). Six samples of combustion state data were collected using two distinct types of burners to facilitate the training and validation of GA-DBN. The proposed methodology leverages RQA to extract intricate patterns and dynamic features from time series data representing combustion behavior. By quantifying the recurrence plot of specific patterns, the analysis provides valuable insights into the underlying thermoacoustic dynamics. Among three different feature extraction methods, RQA stands out remarkably in performance. These RQA-derived features serve as input to a carefully tuned DBN, which is trained to learn the complex relationships within the combustion process. The classification accuracy of deep belief network optimized by genetic algorithm (GA-DBN) reached an impressive 99.8%. Subsequent multiple comparisons were conducted between GA-DBN, DBN, and support vector machine (SVM), revealing that GA-DBN consistently demonstrated satisfactory classification results. This method holds significant importance in monitoring intricate combustion states.

Nonlinear and nonstationary detection and quantification of multi-scale measured signals for bridge structure

The assessment of nonlinear and nonstationary levels in measured bridge signals is a vital step in system identification and long-term health monitoring for the bridge structure. The field-measured signals from the bridge structure are inherently weak and multiscale, so a specific adaptive variational mode decomposition (AVMD) is proposed to decompose them and extract their included multi-scale features. Combination the adaptability of empirical mode decomposition with the dimensionality reduction of principal component analysis, the number of inherent mode functions (IMFs) that need to be given in the conventional variational mode decomposition is adaptively determined in the proposed AVMD. The original measured signals from the bridge structure multiscale are subsequently decomposed by AVMD into the multiscale IMFs with the lowest cross-correlation. Then, the recurrence plot and recurrence quantification analysis are introduced into the detection and quantification of the measured signals, and the nonlinear and nonstationary quantification indexes are constructed to describe quantitatively the nonlinear and nonstationary levels. The stabilities and accuracies of three nonlinear and three nonstationary quantification indexes are comparatively discussed by the nonlinear and nonstationary detection and quantification of three well-defined simulated signals. The Shannon entropy and trapping time indexes are subsequently determined to quantify the nonlinear and nonstationary levels of the measured signals, respectively. Finally, the proposed algorithm and quantification indexes are applied to the nonlinear and nonstationary detection and quantification of the measured signals from the real-world bridge structures. It is shown from the validation and discussion that the proposed algorithm is available to detect and quantify the nonlinear and nonstationary levels of the measured multiscale signal from the real-world bridge structure.

Detecting Artificial Intelligence-Generated Personal Statements in Professional Physical Therapist Education Program Applications: A Lexical Analysis.

The objective of this study was to compare the lexical sophistication of personal statements submitted by professional physical therapist education program applicants with those generated by OpenAI's Chat Generative Pre-trained Transformer (ChatGPT). Personal statements from 152 applicants and 20 generated by ChatGPT were collected, all in response to a standardized prompt. These statements were coded numerically, then analyzed with recurrence quantification analyses (RQAs). RQA indices including recurrence, determinism, max line, mean line, and entropy were compared with t tests. A receiver operating characteristic (ROC) curve analysis was used to examine discriminative validity of RQA indices to distinguish between ChatGPT and human-generated personal statements. ChatGPT-generated personal statements exhibited higher recurrence, determinism, mean line, and entropy values than did human-generated personal statements. The strongest discriminator was a 13.04% determinism rate, which differentiated ChatGPT from human-generated writing samples with 70% sensitivity and 91.4% specificity (positive likelihood ratio = 8.14). Personal statements with determinism rates exceeding 13% were 8 times more likely to have been ChatGPT than human generated. While RQA can distinguish artificial intelligence-generated text from human-generated text, it is not absolute. Thus, artificial intelligence introduces additional challenges to the authenticity and utility of personal statements. Admissions committees along with organizations providing guidelines in professional physical therapist education program admissions should re-evaluate the role of personal statements in applications. As artificial intelligence-driven chatbots like ChatGPT complicate the evaluation of personal statements, RQA emerges as a potential tool for admissions committees to detect artificial intelligence-generated statements.

Human versus Machine Intelligence: Assessing Natural Language Generation Models through Complex Systems Theory.

The introduction of Transformer architectures - with the self-attention mechanism - in automatic Natural Language Generation (NLG) is a breakthrough in solving general task-oriented problems, such as the simple production of long text excerpts that resemble ones written by humans. While the performance of GPT-X architectures is there for all to see, many efforts are underway to penetrate the secrets of these black-boxes in terms of intelligent information processing whose output statistical distributions resemble that of natural language. In this work, through the complexity science framework, a comparative study of the stochastic processes underlying the texts produced by the English version of GPT-2 with respect to texts produced by human beings, notably novels in English and programming codes, is offered. The investigation, of a methodological nature, consists first of all of an analysis phase in which the Multifractal Detrended Fluctuation Analysis and the Recurrence Quantification Analysis - together with Zipf's law and approximate entropy - are adopted to characterize long-term correlations, regularities and recurrences in human and machine-produced texts. Results show several peculiarities and trends in terms of long-range correlations and recurrences in the last case. The synthesis phase, on the other hand, uses the complexity measures to build synthetic text descriptors - hence a suitable text embedding - which serve to constitute the features for feeding a machine learning system designed to operate feature selection through an evolutionary technique. Using multivariate analysis, it is then shown the grouping tendency of the three analyzed text types, allowing to place GTP-2 texts in between natural language texts and computer codes. Similarly, the classification task demonstrates that, given the high accuracy obtained in the automatic discrimination of text classes, the proposed set of complexity measures is highly informative. These interesting results allow us to add another piece to the theoretical understanding of the surprising results obtained by NLG systems based on deep learning and let us to improve the design of new informetrics or text mining systems for text classification, fake news detection, or even plagiarism detection.