Determining embedding dimension for phase-space reconstruction using a geometrical construction

Scanning acoustic microscopy for biomechanical characterization of reindeer antler using singular spectral analysis

Scanning Acoustic Microscopy (SAM) has become a vital tool in materials science and biology, allowing for non-destructive and non-invasive analysis of biological specimens and bio-inspired materials. Its deep-penetrating imaging capabilities enable a broad range of applications. This study combines SAM with Singular Spectral Analysis (SSA) to enhance signal processing and extract key data, particularly acoustic impedance. Reindeer antlers, known for their rapid growth and unique mechanical properties, were chosen as a focus for this method. SAM was used to quantify the specific acoustic impedance, longitudinal stiffness, bulk modulus, and Young's modulus of the material at three orientations (0°, 45°, and 90°). This analysis provides a comprehensive understanding of the directional dependence of its structural behavior, highlighting its orthotropic nature. By analyzing cross-sections along three axes, this study reveals the orthotropic biomechanical properties of reindeer antlers, offering a systematic approach to characterizing biological materials. Their unique strength, resilience, and rapid growth highlight their potential as a sustainable and innovative biomaterial for bioengineering and advanced composites.

Personalized prediction of gait freezing using dynamic mode decomposition

Freezing of gait (FoG) is a common severe gait disorder in patients with advanced Parkinson's disease. The ability to predict the onset of FoG episodes early on allows for timely intervention, which is essential for improving the life quality of patients. Machine learning and deep learning, the current methods, face real-time diagnosis challenges due to comprehensive data processing requirements. Their "black box" nature makes interpreting features and classification boundaries difficult. In this manuscript, we explored a dynamic mode decomposition (DMD)-based approach together with optimal delay embedding time to reconstruct and predict the time evolution of acceleration signals, and introduced a triple index based on DMD to predict and classify FoG. Our predictive analysis shows 86.5% accuracy in classification, and an early prediction ratio of 81.97% with an average early prediction time of 6.13 s. This DMD-based approach has the potential for real-time patient-specific FoG prediction.

Ultralow-Dimensionality Reduction for Identifying Critical Transitions by Spatial-Temporal PCA

Discovering dominant patterns and exploring dynamic behaviors especially critical state transitions and tipping points in high-dimensional time-series data are challenging tasks in study of real-world complex systems, which demand interpretable data representations to facilitate comprehension of both spatial and temporal information within the original data space. This study proposes a general and analytical ultralow-dimensionality reduction method for dynamical systems named spatial-temporal principal component analysis (stPCA) to fully represent the dynamics of a high-dimensional time-series by only a single latent variable without distortion, which transforms high-dimensional spatial information into one-dimensional temporal information based on nonlinear delay-embedding theory. The dynamics of this single variable is analytically solved and theoretically preserves the temporal property of original high-dimensional time-series, thereby accurately and reliably identifying the tipping point before an upcoming critical transition. Its applications to real-world datasets such as individual-specific heterogeneous ICU records demonstrate the effectiveness of stPCA, which quantitatively and robustly provides the early-warning signals of the critical/tipping state on each patient.

Biomechanical Changes During Running on a Lower Body Positive Pressure Treadmill in Competitive Runners

Lower body positive pressure treadmills (LBPPTs) offer precise body weight unloading for injury rehabilitation and performance training in runners. This study investigated biomechanical changes during running at varying body weight support (BWS) levels (0%-80%) in competitive runners, including sex-specific responses. Twenty-six runners (age: 33.6 ± 9.8 years; 15 female, 11 male) completed randomized 3-min running bouts at 12 km/h across nine BWS levels. Spatiotemporal parameters, plantar force, peak tibial acceleration, and running stability were measured using pressure insoles and inertial sensors placed at the tibia and foot. Our results revealed significant reductions in step rate (b = -0.24 steps•min-1/%BWS, p < 0.001), normalized ground contact time (b = -0.001 1/%BWS, p < 0.001), maximum plantar force (b = -0.010 BW/%BWS, p < 0.001), and peak tibial acceleration (b = -0.03 g/%BWS, p < 0.001) with increased BWS. Swing time increased (b = 1.50 ms/%BWS, p < 0.001), while stance time decreased (b = -0.41 ms/%BWS, p < 0.001). Running stability showed marginal changes (foot: b = -0.001 1/%BWS, p = 0.017; tibia: b = 0.001 1/%BWS, p = 0.009). Sex differences were observed in step rate (b = -6.79 steps•min-1, p = 0.045) and maximum plantar force (b = -0.128 BW, p = 0.034), but there were no significant sex × BWS interaction effects for any of the investigated parameters. Findings from this study highlight the effectiveness of LBPPTs for reducing musculoskeletal loading while revealing associated gait changes. Athletes, therapists, and coaches should consider individual biomechanical responses to optimize rehabilitation and performance strategies. Future research should explore long-term adaptations and injury prevention outcomes.

A comparison between novice and elite cyclists movement stability during cycling

The Lyapunov Exponent (LyE) is a non-linear technique that analyses stability, which refers to the capacity of systems to mitigate environmental perturbations. Whether elite athletes have an optimised movement stability is contentious. There has been limited research exploring the differences in movement stability using the LyE between elite and novice athletes. The purpose of this study was to compare movement stability between novice and elite male cyclists across a 4000 m bout, using the LyE. Participants completed two sessions of cycling (familiarisation and testing). Inertial measurement units were attached to the head, thorax, pelvis and left and right shanks to measure segment accelerations. The LyE was calculated using five, 100 cycle intervals across the bout. Elite cyclists had greater segment movement instability compared to novices at the head and pelvis in the longitudinal and medio-lateral direction, thorax in the medio-lateral and anterior-posterior direction and medio-lateral shanks. Both novice and elite cyclists demonstrated increased head, thorax and pelvis movement instability across the bout. This increase in instability across the bout may demonstrate the impact of fatigue on movement stability. Future research needs to now examine movement stability in the velodrome and explore the correlation between movement stability and aerodynamic drag.

The changes in neural complexity and connectivity in thalamocortical and cortico-cortical systems after propofol-induced unconsciousness in different temporal scales

Existing studies have indicated neural activity across diverse temporal and spatial scales. However, the alterations in complexity, functional connectivity, and directional connectivity within the thalamocortical and corticocortical systems across various scales during propofol-induced unconsciousness remain uncertain. We analyzed the stereo-electroencephalography (SEEG) from wakefulness to unconsciousness among the brain regions of the prefrontal cortex, temporal lobe, and anterior nucleus of the thalamus. The complexity (examined by permutation entropy (PE)), functional connectivity (permutation mutual information (PMI)), and directional connectivity (symbolic conditional mutual information (SCMI) and directionality index (DI)) were calculated across various scales. In the lower-band frequency (0.1-45 Hz) SEEG, after the loss of consciousness, PE significantly decreased (p < 0.001) in all regions and scales, except for the thalamus, which remained relatively unchanged at large scales (τ=32 ms). Following the loss of consciousness, inter-regional PMI either significantly increased or remained stable across different scales (τ=4 ms to 32 ms). During the unconscious state, SCMI between brain regions exhibited inconsistent changes across scales. In the late unconscious stage, the inter-regional DI across all scales indicated a shift from a balanced state of information flow between brain regions to a pattern where the prefrontal cortex and thalamus drive the temporal lobe. Our findings demonstrate that propofol-induced unconsciousness is associated with reduced cortical complexity, diverse functional connectivity, and a disrupted balance of information integration among thalamocortical and cortico-cortical systems. This study enhances the theoretical understanding of anesthetic-induced loss of consciousness by elucidating the scale- and region-specific effects of propofol on thalamocortical and cortico-cortical systems.

Two-phase flow pattern transition behaviors on experimental established ordinal pattern networks

Identifying the flow pattern transition dynamics is a fundamental challenge in modeling a two-phase flow system. In this paper, we investigate the gas-liquid two-phase flow pattern transition behaviors with analyzing the topology structures of the experimental established gas-liquid two-phase flow complex networks. First, we carry out a series of gas-liquid two-phase flow experiments in a vertical 50 mm inner diameter pipe. During the experiments, the two-phase flow fluctuation signals are collected and used to establish the ordinal pattern complex networks, which represent different flow patterns. Then, we employ a K-core decomposition method to identify the hierarchical structures of our established flow pattern networks. We find that the decay rate of the K-core size is sensitive to the flow conditions and can be a potential metric for identifying the flow pattern transitions. Additionally, we analyze the network homology persistence, which indicates the loop structures in the flow pattern networks. The persistence indexes-maximum persistence and persistence entropy-are used to investigate the flow pattern oscillatory behaviors along with the flow pattern transitions. This research provides a novel way for investigating the flow pattern transition behaviors of a gas-liquid two-phase flow system, which are expected to be applicable in other complex fluid systems.

Multiple Sclerosis Classification Using the Local Divergence Exponent: Parameters Selection for State-Space Reconstruction

BACKGROUND

Using the local divergence exponent (LDE), it has been concluded that walking stability is impaired in people with multiple sclerosis (pwMS). However, the use of several calculation approaches hinders comparisons across studies. We aimed to determine whether using different parameters for state space reconstruction to calculate LDE affects the classification of pwMS.

METHODS

A total of 55 pwMS and 23 controls walked up and down a 20 m corridor for 5 min. The LDE was calculated using three different combinations of n-dimensions (dE) and time delays (τ): (a) trial-specific, (b) median across subjects, and (c) fixed dE = 5 and τ = 10. The LDE was calculated using vertical (VT), mediolateral (ML), and anteroposterior (AP) accelerations, the norm (N), and 3D data from sensors placed on the sternum and lumbar. Classification accuracy across results obtained with different parameter combinations was compared using a Quadratic Discriminant Analysis (QDA).

RESULTS

The best classification accuracy, 84%, was achieved when using the LDE obtained with norm acceleration data from the sternum sensor with a fixed dE = 5 and τ = 10 and considering speed as a covariate. Lumbar LDEs were less accurate than sternum LDEs.

CONCLUSIONS

LDEs calculated with a fixed dE = 5 and τ = 10 for the norm acceleration from a sternum-placed sensor can best classify pwMS. Using fixed parameters for the state space reconstruction, and consequently LDE calculation, can simplify the implementation of the LDE as a mobility biomarker in MS and provides evidence for future consensus for its calculation.

Recurrence Quantification Analysis for Scene Change Detection and Foreground/Background Segmentation in Videos

This paper presents the mathematical framework of Recurrence Quantification Analysis (RQA) for dynamic video processing, exploring its applications in two primary tasks: scene change detection and adaptive foreground/background segmentation. Originally developed for time series analysis, Recurrence Quantification Analysis (RQA) examines the recurrence of states within a dynamic system. When applied to video streams, RQA detects recurrent patterns by leveraging the temporal dynamics of video frames. This approach offers a computationally efficient and robust alternative to traditional deep learning methods, which often demand extensive training data and high computational power. Our approach is evaluated on three annotated video datasets: Autoshot, RAI, and BBC Planet Earth, where it demonstrates effectiveness in detecting abrupt scene changes, achieving results comparable to state-of-the-art techniques. We also apply RQA to foreground/background segmentation using the UCF101 and DAVIS datasets, where it accurately distinguishes between foreground motion and static background regions. Through the examination of heatmaps based on the embedding dimension and Recurrence Plots (RPs), we show that RQA provides precise segmentation, with RPs offering clearer delineation of foreground objects. Our findings indicate that RQA is a promising, flexible, and computationally efficient approach to video analysis, with potential applications across various domains requiring dynamic video processing.

Sex-specific trunk movement coordination in participants with low-back pain and asymptomatic controls

Background

Trunk posture and lumbo-pelvic coordination can influence spinal loading and are commonly used as clinical measures in the diagnosis and management of low-back pain and injury risk. However, sex and pain specific characteristics have rarely been investigated in a large cohort of both healthy individuals and low-back pain patients. It has also been suggested that the motor control of trunk stability and trunk movement variability is altered in individuals with low-back pain, with possible implications for pain progression. Nonetheless, clear links to low-back pain are currently lacking.

Objective

To investigate trunk posture, lumbo-pelvic coordination, trunk dynamic stability and trunk movement variability in an adequately large cohort of individuals with low-back pain and asymptomatic controls and to explore specific effects of sex, pain intensity and pain chronicity.

Methods

We measured lumbo-pelvic kinematics during trunk flexion and trunk dynamic stability and movement variability during a cyclic pointing task in 306 adults (156 females) aged between 18 and 64 years, reporting either no low-back pain or pain in the lumbar area of the trunk. Participants were grouped based on their characteristic pain intensity as asymptomatic (ASY, N = 53), low to medium pain (LMP, N = 185) or medium to high pain (MHP, N = 68). Participants with low-back pain that persisted for 12 weeks or longer were categorized as chronic (N = 104). Data were analyzed using linear mixed models in the style of a two way anova.

Results

Female participants showed a higher range of motion in both the trunk and pelvis during trunk flexion, as well as an increased lumbar lordosis in standing attributed to a higher pelvic angle that persisted throughout the entire trunk flexion movement, resulting in a longer duration of lumbar lordosis. The intensity and chronicity of the pain had a negligible effect on trunk posture and the lumbo-pelvic coordination. Pain chronicity had an effect on trunk dynamic stability (i.e., increased trunk instability), while no effects of sex and pain intensity were detected in trunk dynamic stability and movement variability.

Conclusions

Low-back pain intensity and chronicity was not associated with lumbo-pelvic posture and kinematics, indicating that lumbo-pelvic posture and kinematics during a trunk flexion movement have limited practicality in the clinical diagnosis and management of low-back pain. On the other hand, the increased local instability of the trunk during the cyclic coordination task studied indicates control errors in the regulation of trunk movement in participants with chronic low-back pain and could be considered a useful diagnostic tool in chronic low-back pain.

DIAGNOSIS OF HEART FAILURE BASED ON THE PHASE SPACE COMPLEXITY OF BALLISTOCARDIOGRAM WITH ENSEMBLE EMPIRICAL MODE DECOMPOSITION

This study introduced a novel auxiliary method for heart failure (HF) diagnosis using the phase space complexity features of ballistocardiogram (BCG) signals collected from piezoelectric sensors. Such a method can potentially monitor high-risk patients out of the clinic. Experimental measurements were collected from 46 patients with HF and 24 healthy subjects. The signals were divided into 1014 nonoverlapping segments (HF: 684 segments, Healthy: 330 segments). First, a digital signal processing framework was established to extract phase space complexity features of BCG with ensemble empirical mode decomposition. Applying a targeted selection strategy, we then identified three key intrinsic mode function (IMF) bands (IMF4–IMF6) for subsequent analysis. Different IMF combinations of features were evaluated using the K-Nearest Neighbors (KNN), Support Vector Machine (SVM), Random Forest (RF), and eXtreme Gradient Boosting (XGB) approaches. Through 10-fold cross-validation, the proposed method exhibited 94.98%, 93.80%, 94.76%, and 94.86% accuracies for the KNN, SVM, RF, and XGB classifiers, respectively. The best performance was achieved by combining IMF4–IMF6 features with the KNN classifier. The proposed BCG signal processing framework is lucrative for diagnosing HF in a home setting.

The inhibitory effect of intraspinal microstimulation of the sacral spinal cord on nonlinear bladder reflex dynamics in cats

Objective

Electrical stimulation of the pudendal nerve, pelvic nerve, sacral dorsal root ganglion (DRG), and spinal cord has been explored to treat urinary incontinence and overactive bladder (OAB). This study introduces sacral intraspinal microstimulation (ISMS) as a novel method to inhibit spontaneous bladder reflexes in anesthetized cats. In addition, we investigated the effects of intermittent and switching stimulation patterns on bladder inhibition.

Methods

The electrode was implanted in the dorsal horn of the S2 spinal cord. Bladder pressure was recorded under isovolumetric conditions, and the stimulation parameters were adjusted to inhibit spontaneous bladder contractions. Nonlinear dynamic methods, including chaos theory, were employed to analyze the complexity of bladder reflexes.

Results

Results demonstrated that ISMS targeting the dorsal horn of the S2 spinal segment effectively suppressed high-amplitude spontaneous contractions. Furthermore, bladder reflexes exhibited complex dynamics, ranging from regular to chaotic patterns, with transitions between these states. Importantly, ISMS was able to stabilize these chaotic dynamics, leading to more controlled bladder behavior.

Conclusion

These findings suggest that sacral ISMS offers a promising, targeted alternative to traditional stimulation therapies, potentially providing a new therapeutic approach for managing OAB and urinary incontinence by regulating chaotic bladder activity.

Reservoir computing approaches to unsupervised concept drift detection in dynamical systems

While the assumption that dynamical systems are stationary is common for modeling purposes, in reality, this is rarely the case. Rather, these systems can change over time, a phenomenon referred to as concept drift in the modeling community. While there exist numerous statistics-based methods for concept drift detection on stochastic processes, approaches leveraging nonlinear time series analysis (NTSA) are rarer but seeing increased focus in cases where the processes are deterministic. In this work, we propose a novel approach to unsupervised concept drift detection in dynamical systems utilizing the embedding offered by a reservoir computing (RC) model. This approach is inspired by the performance of RC on supervised classification tasks that indicates a strong ability to characterize dynamical systems. We assess this method on a number of synthetic drifting data streams from dynamical systems as well as an experimental case concerning faulty ball bearing. Our results suggest that the RC based methods are able to generally outperform the existing NTSA methods across the test cases. We conclude our work with some comments regarding real-time implementation and the impact of hyper-parameters on the proposed algorithm.

Non-parametric full cross mapping (NFCM): a highly-stable measure for causal brain network and a pilot application

Objective.Measuring causal brain network from neurophysiological signals has recently attracted much attention in the field of neuroinformatics. Traditional data-driven algorithms are computationally time-consuming and unstable due to parameter settings.Approach.To resolve these limits, we proposed a novel parameter-free technique, called 'non-parametric full cross mapping (NFCM)'. The NFCM adapts current convergent cross-mapping concept, and makes two improvements: (1) an improved phase-space reconstruction with constant embedding parameters and (2) cross-mapping estimate of all embedding vectors on manifolds following simplex projection.Main results.Numerical experiments verify that our NFCM has the highest quantization stability even when perturbed by system noise, and its coefficient of variation is almost lower than that of the six baseline methods. The developed NFCM is finally used in stereoelectroencephalogram analysis of drug-resistant epilepsy in children (DREC). A total of 36 seizures, comprising 18 surgical successes and 18 failures, were included to explore the brain network dynamics. The average causal coupling in epileptogenic zones of successful surgery (0.81 ± 0.04) is significantly higher than that in non-epileptogenic zones (0.40 ± 0.03) withP<0.001via Mann-Whitney-U-test. While there is no significant difference among the 18 failed surgeries.Significance.The causal brain network measured by our NFCM is confirmed as a credible biomarker for localizing epileptogenic zones in DREC. These findings promise to advance precision medicine for DREC.

Recurrence quantification analysis of rs-fMRI data: A method to detect subtle changes in the TgF344-AD rat model

BACKGROUND AND OBJECTIVE

Alzheimer's disease (AD) is one of the leading causes of dementia, affecting the world's population at a growing rate. The preclinical stage of AD lasts over a decade, hence understanding AD-related early neuropathological effects on brain function at this stage facilitates early detection of the disease.

METHODS

Resting-state functional magnetic resonance imaging (rs-fMRI) has been a powerful tool for understanding brain function, and it has been widely used in AD research. In this study, we apply Recurrence Quantification Analysis (RQA) on rs-fMRI images of 4-months (4 m) and 6-months-old (6 m) TgF344-AD rats and WT littermates to identify changes related to the AD phenotype and aging. RQA has been focused on areas of the default mode-like network (DMLN) and was performed based on Recurrence Plots (RP). RP is a mathematical representation of any dynamical system that evolves over time as a set of its state recurrences. In this paper, RPs were extracted in order to identify the affected regions of the DMLN at very early stages of AD.

RESULTS

Using the RQA approach, we identified significant changes related to the AD phenotype at 4 m and/or 6 m in several areas of the rat DMLN including the BFB, Hippocampal fields CA1 and CA3, CG1, CG2, PrL, PtA, RSC, TeA, V1, V2. In addition, with age, brain activity of WT rats showed less predictability, while the AD rats presented reduced decline of predictability.

CONCLUSIONS

The results of this study demonstrate that RQA of rs-fMRI data is a potent approach that can detect subtle changes which might be missed by other methodologies due to the brain's non-linear dynamics. Moreover, this study provides helpful information about specific areas involved in AD pathology at very early stages of the disease in a very promising rat model of AD. Our results provide valuable information for the development of early detection methods and novel diagnosis tools for AD.

Generalized synchronization in the presence of dynamical noise and its detection via recurrent neural networks

Given two unidirectionally coupled nonlinear systems, we speak of generalized synchronization when the responder "follows" the driver. Mathematically, this situation is implemented by a map from the driver state space to the responder state space termed the synchronization map. In nonlinear times series analysis, the framework of the present work, the existence of the synchronization map amounts to the invertibility of the so-called cross map, which is a continuous map that exists in the reconstructed state spaces for typical time-delay embeddings. The cross map plays a central role in some techniques to detect functional dependencies between time series. In this paper, we study the changes in the "noiseless scenario" just described when noise is present in the driver, a more realistic situation that we call the "noisy scenario." Noise will be modeled using a family of driving dynamics indexed by a finite number of parameters, which is sufficiently general for practical purposes. In this approach, it turns out that the cross and synchronization maps can be extended to the noisy scenario as families of maps that depend on the noise parameters, and only for "generic" driver states in the case of the cross map. To reveal generalized synchronization in both the noiseless and noisy scenarios, we check the existence of synchronization maps of higher periods (introduced in this paper) using recurrent neural networks and predictability. The results obtained with synthetic and real-world data demonstrate the capability of our method.

Analyzing and identifying predictable time range for stress prediction based on chaos theory and deep learning

Propose

Stress is a common problem globally. Prediction of stress in advance could help people take effective measures to manage stress before bad consequences occur. Considering the chaotic features of human psychological states, in this study, we integrate deep learning and chaos theory to address the stress prediction problem.

Methods

Based on chaos theory, we embed one's seemingly disordered stress sequence into a high dimensional phase space so as to reveal the underlying dynamics and patterns of the stress system, and meanwhile are able to identify the stress predictable time range. We then conduct deep learning with a two-layer (dimension and temporal) attention mechanism to simulate the nonlinear state of the embedded stress sequence for stress prediction.

Results

We validate the effectiveness of the proposed method on the public available Tesserae dataset. The experimental results show that the proposed method outperforms the pure deep learning method and Chaos method in both 2-label and 3-label stress prediction.

Conclusion

Integrating deep learning and chaos theory for stress prediction is effective, and can improve the prediction accuracy over 2% and 8% more than those of the deep learning and the Chaos method respectively. Implications and further possible improvements are also discussed at the end of the paper.

The Combination of Topological Data Analysis and Mathematical Modeling Improves Sleep Stage Prediction From Consumer-Grade Wearables

Wearable devices have become commonplace tools for tracking behavioral and physiological parameters in real-world settings. Nonetheless, the practical utility of these data for clinical and research applications, such as sleep analysis, is hindered by their noisy, large-scale, and multidimensional characteristics. Here, we develop a neural network algorithm that predicts sleep stages by tracking topological features (TFs) of wearable data and model-driven clock proxies (CPs) reflecting the circadian propensity for sleep. To evaluate its accuracy, we apply it to motion and heart rate data from the Apple Watch worn by young subjects undergoing polysomnography (PSG) and compare the predicted sleep stages with the corresponding ground truth PSG records. The neural network that includes TFs and CPs along with raw wearable data as inputs shows improved performance in classifying Wake/REM/NREM sleep. For example, it shows significant improvements in identifying REM and NREM sleep (AUROC/AUPRC improvements >13% and REM/NREM accuracy improvement of 12%) compared with the neural network using only raw data inputs. We find that this improvement is mainly attributed to the heart rate TFs. To further validate our algorithm on a different population, we test it on elderly subjects from the Multi-ethnic Study of Atherosclerosis cohort. This confirms that TFs and CPs contribute to the improvements in Wake/REM/NREM classification. We next compare the performance of our algorithm with previous state-of-the-art wearable-based sleep scoring algorithms and find that our algorithm outperforms them within and across different populations. This study demonstrates the benefits of combining topological data analysis and mathematical modeling to extract hidden inputs of neural networks from puzzling wearable data.

Dynamical systems theory applied to short walking trials

Human walking is an extremely complex neuromuscular activity whose simplicity disappears when an attempt is made to provide a quantitative description of the process. The dynamical systems theory provides a framework for analyzing the stability and chaotic nature of dynamical systems, employing Floquet multipliers (FM) and long and short-term Lyapunov exponents (LE), respectively. This report compares FM and LE from three methods: method A (false nearest neighbors and numerical approximation), method B (false nearest neighbors and semi-analytical technique) and method C (singular value decomposition and semi-analytical technique). Data from 33 healthy older adults with no history of falls were used to explain the dynamic system. A surrogate center of mass trajectory was calculated for the analysis of sway in the transverse plane. Results revealed methodological differences in LE and FM calculations with semi-analytical solutions providing closer approximations to observed gait behavior. The long-term LE from Methods A and B were similar, but other LE pairings differed. Method A's short-term LE indicated chaotic gaits for all subjects, while long-term LE from Methods A and B indicated chaos for half the subjects. Method C showed non-chaotic gait for most subjects. Method B's FM indicated over 30% of subjects had unstable gait. Method C yielded values of LE and FM that most closely matched the subjects' gait patterns. This study offers a methodological foundation for gait analysis using short time-series data, facilitating deeper insights into both stability and chaos within gait dynamics.

Localized electrocortical activity as a function of single-leg squat phases and its relationship to knee frontal plane stability

This study investigated differences in electroencephalography (EEG) activity within motor-related brain areas during three phases of a single-leg squat (SLS)-i.e., descending, holding, and ascending phases. Specifically, utilizing advanced magnetic resonance imaging guided EEG source localization techniques and markerless motion capture technology, we explored the interplay between concurrently recorded lower-extremity biomechanics and brain activity. Among the phases of a nondominant leg SLS, differences in contralateral brain activity (right hemisphere) were found in the activity of the precentral gyrus, the postcentral gyrus, and the sensory motor area. Alternatively, during the dominant SLS leg, differences among the three SLS phases in contralateral brain activity were fewer. Hemispheric dependent brain activity also significantly correlated with participants' knee valgus angle range of motion (right hemisphere) and peak knee valgus angles (left hemisphere). In addition to the novel brain and biomechanical findings, this study sheds light on the technical feasibility of recording EEG during complex multi-joint movements and its potential applications in understanding sensorimotor behavior.

Linear and nonlinear causality in financial markets

Identifying and quantifying co-dependence between financial instruments is a key challenge for researchers and practitioners in the financial industry. Linear measures such as the Pearson correlation are still widely used today, although their limited explanatory power is well known. In this paper, we present a much more general framework for assessing co-dependencies by identifying linear and nonlinear causalities in the complex system of financial markets. To do so, we use two different causal inference methods, transfer entropy and convergent cross-mapping, and employ Fourier transform surrogates to separate their linear and nonlinear contributions. We find that stock indices in Germany and the U.S. exhibit a significant degree of nonlinear causality and that correlation, while a very good proxy for linear causality, disregards nonlinear effects and hence underestimates causality itself. The presented framework enables the measurement of nonlinear causality, the correlation-causality fallacy, and motivates how causality can be used for inferring market signals, pair trading, and risk management of portfolios. Our results suggest that linear and nonlinear causality can be used as early warning indicators of abnormal market behavior, allowing for better trading strategies and risk management.

Coronary Artery Disease Detection Based on a Novel Multi-Modal Deep-Coding Method Using ECG and PCG Signals

Coronary artery disease (CAD) is an irreversible and fatal disease. It necessitates timely and precise diagnosis to slow CAD progression. Electrocardiogram (ECG) and phonocardiogram (PCG), conveying abundant disease-related information, are prevalent clinical techniques for early CAD diagnosis. Nevertheless, most previous methods have relied on single-modal data, restricting their diagnosis precision due to suffering from information shortages. To address this issue and capture adequate information, the development of a multi-modal method becomes imperative. In this study, a novel multi-modal learning method is proposed to integrate both ECG and PCG for CAD detection. Along with deconvolution operation, a novel ECG-PCG coupling signal is evaluated initially to enrich the diagnosis information. After constructing a modified recurrence plot, we build a parallel CNN network to encode multi-modal information, involving ECG, PCG and ECG-PCG coupling deep-coding features. To remove irrelevant information while preserving discriminative features, we add an autoencoder network to compress feature dimension. Final CAD classification is conducted by combining support vector machine and optimal multi-modal features. The experiment is validated on 199 simultaneously recorded ECG and PCG signals from non-CAD and CAD subjects, and achieves high performance with accuracy, sensitivity, specificity and f1-score of 98.49%, 98.57%,98.57% and 98.89%, respectively. The result demonstrates the superiority of the proposed multi-modal method in overcoming information shortages of single-modal signals and outperforming existing models in CAD detection. This study highlights the potential of multi-modal deep-coding information, and offers a wider insight to enhance CAD diagnosis.

Attractor dynamics of elite performance: the high bar longswing

Combining biomechanics and motor control, the aim of this study was to investigate the limit cycle dynamics during the high bar longswing across the UK elite gymnastics pathway age groupings. Senior, junior and development gymnasts (N = 30) performed three sets of eight consecutive longswings on the high bar. The centre of mass motion was examined through Poincaré plots and recurrence quantification analysis exploring the limit cycle dynamics of the longswing. Close to one-dimensional limit cycles were displayed for the senior (correlation dimension (CD) = 1.17 ± .08), junior (CD = 1.26 ± .08) and development gymnasts (CD = 1.33 ± .14). Senior elite gymnasts displayed increased recurrence characteristics in addition to longer longswing duration (p < .01) and lower radial angular velocity of the mass centre (p < .01). All groups of gymnasts had highly recurrent and predictable limit cycle characteristics. The findings of this research support the postulation that the further practice, experience and individual development associated with the senior gymnasts contribute to the refinement of the longswing from a nonlinear dynamics perspective. These findings support the idea of functional task decomposition informing the understanding of skill and influencing coaches' decisions around skill development and physical preparation.

EEG spectral attractors identify a geometric core of brain dynamics

Multidimensional reconstruction of brain attractors from electroencephalography (EEG) data enables the analysis of geometric complexity and interactions between signals in state space. Utilizing resting-state data from young and older adults, we characterize periodic (traditional frequency bands) and aperiodic (broadband exponent) attractors according to their geometric complexity and shared dynamical signatures, which we refer to as a geometric cross-parameter coupling. Alpha and aperiodic attractors are the least complex, and their global shapes are shared among all other frequency bands, affording alpha and aperiodic greater predictive power. Older adults show lower geometric complexity but greater coupling, resulting from dedifferentiation of gamma activity. The form and content of resting-state thoughts were further associated with the complexity of attractor dynamics. These findings support a process-developmental perspective on the brain's dynamic core, whereby more complex information differentiates out of an integrative and global geometric core.

Revealing alterations in heart rate fluctuations during the progression of Chagas disease

Introduction

The heart rate variability (HRV) continually evolves throughout life, reflecting modifications in the architecture of the sinoatrial node (SAN) and in the regulation of heart rate by the autonomic nervous system (ANS). Both can be considerably affected by Chagas disease, causing important changes in the complex nature of HRV. We aim to evaluate the ability of an index based on the false nearest neighbors method (FN10) to reflect these changes during disease progression.

Methods

We perform a retrospective, descriptive, and cross-sectional study analyzing HRV time series of participants with Chagas disease. We determine the dependence of FN10 on age and sex in a healthy population, and then evaluate FN10 in individuals with Chagas disease.

Results and discussion

In the healthy population, FN10 has a scaling behavior with age, which is independent of sex. In Chagas disease, some individuals show FN10 values significantly above those seen in the healthy population. We relate the findings to the pathophysiological mechanisms that determine the progression of the disease. The results indicate that FN10 may be a candidate prognostic biomarker for heart disease.

Postural control depends on early visual experience

The present study investigated the role of early visual experience in the development of postural control (balance) and locomotion (gait). In a cross-sectional design, balance and gait were assessed in 59 participants (ages 7-43 years) with a history of (a) transient congenital blindness, (b) transient late-onset blindness, (c) permanent congenitally blindness, or (d) permanent late-onset blindness, as well as in normally sighted controls. Cataract-reversal participants who experienced a transient phase of blindness and gained sight through cataract removal surgery showed worse balance performance compared with sighted controls even when tested with eyes closed. Individuals with reversed congenital cataracts performed worse than individuals with reversed developmental (late emerging) cataracts. Balance performance in congenitally cataract-reversal participants when tested with eyes closed was not significantly different from that in permanently blind participants. In contrast, their gait parameters did not differ significantly from those of sighted controls. The present findings highlight both the need for visual calibration of proprioceptive and vestibular systems and the crossmodal adaptability of locomotor functions.

Quantifying instability in neurological disorders EEG based on phase space DTM function

Classifying individuals with neurological disorders and healthy subjects using EEG is a crucial area of research. The current feature extraction approach focuses on the frequency domain features in each of the EEG frequency bands and functional brain networks. In recent years, researchers have discovered and extensively studied stability differences in the electroencephalograms (EEG) of patients with neurological disorders. Based on this, this paper proposes a feature descriptor to characterize EEG instability. The proposed method starts by forming a signal point cloud through Phase Space Reconstruction (PSR). Subsequently, a pseudo-metric space is constructed, and pseudo-distances are calculated based on the consistent measure of the point cloud. Finally, Distance to Measure (DTM) Function are generated to replace the distance function in the original metric space. We calculated the relative distances in the point cloud by measuring signal similarity and, based on this, summarized the point cloud structures formed by EEG with different stabilities after PSR. This process demonstrated that Multivariate Kernel Density Estimation (MKDE) based on a Gaussian kernel can effectively separate the mappings of different stable components within the signal in the phase space. The two average DTM values are then proposed as feature descriptors for EEG instability.In the validation phase, the proposed feature descriptor is tested on three typical neurological disorders: epilepsy, Alzheimer's disease, and Parkinson's disease, using the Bonn dataset, CHB-MIT, the Florida State University dataset, and the Iowa State University dataset. DTM values are used as feature inputs for four different machine learning classifiers, and The results show that the best classification accuracy of the proposed method reaches 98.00 %, 96.25 %, 96.71 % and 95.34 % respectively, outperforming commonly used nonlinear descriptors. Finally, the proposed method is tested and analyzed using noisy signals, demonstrating its robustness compared to other methods.

An algorithm for simplified recurrence analysis

Recurrence analysis applications are hindered by several issues including the selection of critical parameters, noise sensitivity, computational complexity, or the analysis of non-stationary systems. Great progresses have been made by the community to address these issues individually, yet the diversity of resulting techniques with often additional parameters as well as a lack of consensus still impedes its use by nonspecialists. We present a procedure for simplified recurrence analysis based on compact recurrence plots with automatized parameter selection and enhanced noise robustness, and that are suited to the analysis of complex non-stationary systems. This approach aims at supporting the expansion of recurrence analysis for currently challenging or future applications such as for large systems, on-site studies, or using machine learning. The method is demonstrated on both synthetic and real data showing promising results.

Classification of BCI-EEG Based on the Augmented Covariance Matrix

OBJECTIVE

Electroencephalography signals are recorded as multidimensional datasets. We propose a new framework based on the augmented covariance that stems from an autoregressive model to improve motor imagery classification.

METHODS

From the autoregressive model can be derived the Yule-Walker equations, which show the emergence of a symmetric positive definite matrix: the augmented covariance matrix. The state-of the art for classifying covariance matrices is based on Riemannian Geometry. A fairly natural idea is therefore to apply this Riemannian Geometry based approach to these augmented covariance matrices. The methodology for creating the augmented covariance matrix shows a natural connection with the delay embedding theorem proposed by Takens for dynamical systems. Such an embedding method is based on the knowledge of two parameters: the delay and the embedding dimension, respectively related to the lag and the order of the autoregressive model. This approach provides new methods to compute the hyper-parameters in addition to standard grid search.

RESULTS

The augmented covariance matrix performed ACMs better than any state-of-the-art methods. We will test our approach on several datasets and several subjects using the MOABB framework, using both within-session and cross-session evaluation.

CONCLUSION

The improvement in results is due to the fact that the augmented covariance matrix incorporates not only spatial but also temporal information. As such, it contains information on the nonlinear components of the signal through the embedding procedure, which allows the leveraging of dynamical systems algorithms.

SIGNIFICANCE

These results extend the concepts and the results of the Riemannian distance based classification algorithm.

Unlocking Predictive Capability and Enhancing Sensing Performances of Plasmonic Hydrogen Sensors via Phase Space Reconstruction and Convolutional Neural Networks

This study innovates plasmonic hydrogen sensors (PHSs) by applying phase space reconstruction (PSR) and convolutional neural networks (CNNs), overcoming previous predictive and sensing limitations. Utilizing a low-cost and efficient colloidal lithography technique, palladium nanocap arrays are created and their spectral signals are transformed into images using PSR and then trained using CNNs for predicting the hydrogen level. The model achieves accurate predictions with average accuracies of 0.95 for pure hydrogen and 0.97 for mixed gases. Performance improvements observed are a reduction in response time by up to 3.7 times (average 2.1 times) across pressures, SNR increased by up to 9.3 times (average 3.9 times) across pressures, and LOD decreased from 16 Pa to an extrapolated 3 Pa, a 5.3-fold improvement. A practical application of remote hydrogen sensing without electronics in hydrogen environments is actualized and achieves a 0.98 average test accuracy. This methodology reimagines PHS capabilities, facilitating advancements in hydrogen monitoring technologies and intelligent spectrum-based sensing.

Intelligent Fault Diagnosis Method for Rotating Machinery Based on Recurrence Binary Plot and DSD-CNN

To tackle the issue of the traditional intelligent diagnostic algorithm's insufficient utilization of correlation characteristics within the time series of fault signals and to meet the challenges of accuracy and computational complexity in rotating machinery fault diagnosis, a novel approach based on a recurrence binary plot (RBP) and a lightweight, deep, separable, dilated convolutional neural network (DSD-CNN) is proposed. Firstly, a recursive encoding method is used to convert the fault vibration signals of rotating machinery into two-dimensional texture images, extracting feature information from the internal structure of the fault signals as the input for the model. Subsequently, leveraging the excellent feature extraction capabilities of a lightweight convolutional neural network embedded with attention modules, the fault diagnosis of rotating machinery is carried out. The experimental results using different datasets demonstrate that the proposed model achieves excellent diagnostic accuracy and computational efficiency. Additionally, compared with other representative fault diagnosis methods, this model shows better anti-noise performance under different noise test data, and it provides a reliable and efficient reference solution for rotating machinery fault-classification tasks.

Implicit learning provides advantage over explicit learning for gait-cognitive dual-task interference

Dual-task performance holds significant relevance in real-world scenarios. Implicit learning is a possible approach for improving dual-task performance. Analogy learning, utilizing a single metaphor to convey essential information about motor skills, has emerged as a practical method for fostering implicit learning. However, evidence supporting the effect of implicit learning on gait-cognitive dual-task performance is insufficient. This exploratory study aimed to examine the effects of implicit and explicit learning on dual-task performance in both gait and cognitive tasks. Tandem gait was employed on a treadmill to assess motor function, whereas serial seven subtraction tasks were used to gauge cognitive performance. Thirty healthy community-dwelling older individuals were randomly assigned to implicit or explicit learning groups. Each group learned the tandem gait task according to their individual learning styles. The implicit learning group showed a significant improvement in gait performance under the dual-task condition compared with the explicit learning group. Furthermore, the implicit learning group exhibited improved dual-task interference for both tasks. Our findings suggest that implicit learning may offer greater advantages than explicit learning in acquiring autonomous motor skills. Future research is needed to uncover the mechanisms underlying implicit learning and to harness its potential for gait-cognitive dual-task performance in clinical settings.

Estimation of Carleman operator from a univariate time series

Reconstructing a nonlinear dynamical system from empirical time series is a fundamental task in data-driven analysis. One of the main challenges is the existence of hidden variables; we only have records for some variables, and those for hidden variables are unavailable. In this work, the techniques for Carleman linearization, phase-space embedding, and dynamic mode decomposition are integrated to rebuild an optimal dynamical system from time series for one specific variable. Using the Takens theorem, the embedding dimension is determined, which is adopted as the dynamical system's dimension. The Carleman linearization is then used to transform this finite nonlinear system into an infinite linear system, which is further truncated into a finite linear system using the dynamic mode decomposition technique. We illustrate the performance of this integrated technique using data generated by the well-known Lorenz model, the Duffing oscillator, and empirical records of electrocardiogram, electroencephalogram, and measles outbreaks. The results show that this solution accurately estimates the operators of the nonlinear dynamical systems. This work provides a new data-driven method to estimate the Carleman operator of nonlinear dynamical systems.

A rigorous and versatile statistical test for correlations between stationary time series

In disciplines from biology to climate science, a routine task is to compute a correlation between a pair of time series and determine whether the correlation is statistically significant (i.e., unlikely under the null hypothesis that the time series are independent). This problem is challenging because time series typically exhibit autocorrelation and thus cannot be properly analyzed with the standard iid-oriented statistical tests. Although there are well-known parametric tests for time series, these are designed for linear correlation statistics and thus not suitable for the increasingly popular nonlinear correlation statistics. There are also nonparametric tests that can be used with any correlation statistic, but for these, the conditions that guarantee correct false positive rates are either restrictive or unclear. Here, we describe the truncated time-shift (TTS) test, a nonparametric procedure to test for dependence between 2 time series. We prove that this test correctly controls the false positive rate as long as one of the time series is stationary, a minimally restrictive requirement among current tests. The TTS test is versatile because it can be used with any correlation statistic. Using synthetic data, we demonstrate that this test performs correctly even while other tests suffer high false positive rates. In simulation examples, simple guidelines for parameter choices allow high statistical power to be achieved with sufficient data. We apply the test to datasets from climatology, animal behavior, and microbiome science, verifying previously discovered dependence relationships and detecting additional relationships.

The effects of trunk endurance training on running kinematics and its variability in novice female runners

The functional importance of trunk muscle strength for running movement is widely recognised, but the kinematic effects of undertaking specific training are unclear. This study investigated the change in joint angle and its variability during running following trunk muscle training. Eighteen young female and novice runners participated. Using Plug-in-gait model with infrared markers attached to the body surface, the lower limb and lumber angles during running were measured, and the variability was examined by calculating the coefficient variation and Lyapunov exponent. Measurements of trunk endurance were also performed. Over four weeks of training, the subjects performed trunk muscle endurance trainings three times a week. Following this intervention, trunk endurance was found to have significantly increased. The Lyapunov exponent of lumbar flexion-extension angle also significantly increased. Moreover, a decreased range of the ankle angle and increased range of the hip angle were observed following the training. These results demonstrate that the trunk training promoted adjustments to lumbar movement and altered the movement patterns of the participants' lower limbs during running.

Effects of metronome walking on long-term attractor divergence and correlation structure of gait: a validation study in older people

This study investigates the effects of metronome walking on gait dynamics in older adults, focusing on long-range correlation structures and long-range attractor divergence (assessed by maximum Lyapunov exponents). Sixty older adults participated in indoor walking tests with and without metronome cues. Gait parameters were recorded using two triaxial accelerometers attached to the lumbar region and to the foot. We analyzed logarithmic divergence of lumbar acceleration using Rosenstein's algorithm and scaling exponents for stride intervals from foot accelerometers using detrended fluctuation analysis (DFA). Results indicated a concomitant reduction in long-term divergence exponents and scaling exponents during metronome walking, while short-term divergence remained largely unchanged. Furthermore, long-term divergence exponents and scaling exponents were significantly correlated. Reliability analysis revealed moderate intrasession consistency for long-term divergence exponents, but poor reliability for scaling exponents. Our results suggest that long-term divergence exponents could effectively replace scaling exponents for unsupervised gait quality assessment in older adults. This approach may improve the assessment of attentional involvement in gait control and enhance fall risk assessment.

Time-series-analysis-based detection of critical transitions in real-world non-autonomous systems

Real-world non-autonomous systems are open, out-of-equilibrium systems that evolve in and are driven by temporally varying environments. Such systems can show multiple timescale and transient dynamics together with transitions to very different and, at times, even disastrous dynamical regimes. Since such critical transitions disrupt the systems' intended or desired functionality, it is crucial to understand the underlying mechanisms, to identify precursors of such transitions, and to reliably detect them in time series of suitable system observables to enable forecasts. This review critically assesses the various steps of investigation involved in time-series-analysis-based detection of critical transitions in real-world non-autonomous systems: from the data recording to evaluating the reliability of offline and online detections. It will highlight pros and cons to stimulate further developments, which would be necessary to advance understanding and forecasting nonlinear behavior such as critical transitions in complex systems.

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.

Model adaptive phase space reconstruction

Phase space reconstruction (PSR) methods allow for the analysis of low-dimensional data with methods from dynamical systems theory, but their application to prediction models, such as those from machine learning (ML), is limited. Therefore, we here present a model adaptive phase space reconstruction (MAPSR) method that unifies the process of PSR with the modeling of the dynamical system. MAPSR is a differentiable PSR based on time-delay embedding and enables ML methods for modeling. The quality of the reconstruction is evaluated by the prediction loss. The discrete-time signal is converted into a continuous-time signal to achieve a loss function, which is differentiable with respect to the embedding delays. The delay vector, which stores all potential embedding delays, is updated along with the trainable parameters of the model to minimize prediction loss. Thus, MAPSR does not rely on any threshold or statistical criterion for determining the dimension and the set of delay values for the embedding process. We apply the MAPSR method to uni- and multivariate time series stemming from chaotic dynamical systems and a turbulent combustor. We find that for the Lorenz system, the model trained with the MAPSR method is able to predict chaotic time series for nearly seven to eight Lyapunov time scales, which is found to be much better compared to other PSR methods [AMI-FNN (average mutual information-false nearest neighbor) and PECUZAL (Pecora-Uzal) methods]. For the univariate time series from the turbulent combustor, the long-term cumulative prediction error of the MAPSR method for the regime of chaos stays between other methods, and for the regime of intermittency, MAPSR outperforms other PSR methods.

Major depressive disorder recognition by quantifying EEG signal complexity using proposed APLZC and AWPLZC

BACKGROUND

Seeking objective quantitative indicators is important for accurately recognizing major depressive disorder (MDD). Lempel-Ziv complexity (LZC), employed to characterize neurological disorders, faces limitations in tracking dynamic changes in EEG signals due to defects in the coarse-graining process, hindering its precision for MDD objective quantitative indicators.

METHODS

This work proposed Adaptive Permutation Lempel-Ziv Complexity (APLZC) and Adaptive Weighted Permutation Lempel-Ziv Complexity (AWPLZC) algorithms by refining the coarse-graining process and introducing weight factors to effectively improve the precision of LZC in characterizing EEGs and further distinguish MDD patients better. APLZC incorporated the ordinal pattern, while False Nearest Neighbor and Mutual Information algorithms were introduced to determine and adjust key parameters adaptively. Furthermore, we proposed AWPLZC by assigning different weights to each pattern based on APLZC. Thirty MDD patients and 30 healthy controls (HCs) were recruited and their 64-channel resting EEG signals were collected. The complexities of gamma oscillations were then separately computed using LZC, APLZC, and AWPLZC algorithms. Subsequently, a multi-channel adaptive K-nearest neighbor model was constructed for identifying MDD patients and HCs.

RESULTS

LZC, APLZC, and AWPLZC algorithms achieved accuracy rates of 78.29 %, 90.32 %, and 95.13 %, respectively. Sensitivities reached 67.96 %, 85.04 %, and 98.86 %, while specificities were 88.62 %, 95.35 %, and 89.92 %, respectively. Notably, AWPLZC achieved the best performance in accuracy and sensitivity, with a specificity limitation.

LIMITATION

The sample size is relatively small.

CONCLUSION

APLZC and AWPLZC algorithms, particularly AWPLZC, demonstrate superior effectiveness in differentiating MDD patients from HCs compared with LZC. These findings hold significant clinical implications for MDD diagnosis.

Application of next-generation reservoir computing for predicting chaotic systems from partial observations

Next-generation reservoir computing is a machine-learning approach that has been recently proposed as an effective method for predicting the dynamics of chaotic systems. So far, this approach has been applied mainly under the assumption that all components of the state vector of dynamical systems are observable. Here we study the effectiveness of this method when only a scalar time series is available for observation. As illustrations, we use the time series of Rössler and Lorenz systems, as well as the chaotic time series generated by an electronic circuit. We found that prediction is only effective if the feature vector of a nonlinear autoregression algorithm contains monomials of a sufficiently high degree. Moreover, the prediction can be improved by replacing monomials with Chebyshev polynomials. Next-generation models, built on the basis of partial observations, are suitable not only for short-term forecasting, but are also capable of reproducing the long-term climate of chaotic systems. We demonstrate the reconstruction of the bifurcation diagram of the Rössler system and the return maps of the Lorenz and electronic circuit systems.

Emergence of order from chaos through a continuous phase transition in a turbulent reactive flow system

As the Reynolds number is increased, a laminar fluid flow becomes turbulent, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive flow system, as we increase the Reynolds number, we observe the emergence of a single dominant timescale in the acoustic pressure fluctuations, as indicated by its loss of multifractality. Such emergence of order from chaos is intriguing. We perform experiments in a turbulent reactive flow system consisting of flame, acoustic, and hydrodynamic subsystems interacting nonlinearly. We study the evolution of short-time correlated dynamics between the acoustic field and the flame in the spatiotemporal domain of the system. The order parameter, defined as the fraction of the correlated dynamics, increases gradually from zero to one. We find that the susceptibility of the order parameter, correlation length, and correlation time diverge at a critical point between chaos and order. Our results show that the observed emergence of order from chaos is a continuous phase transition. Moreover, we provide experimental evidence that the critical exponents characterizing this transition fall in the universality class of directed percolation. Our paper demonstrates how a real-world complex, nonequilibrium turbulent reactive flow system exhibits universal behavior near a critical point.

Recurrence plot embeddings as short segment nonlinear features for multimodal speaker identification using air, bone and throat microphones

Speech is produced by a nonlinear, dynamical Vocal Tract (VT) system, and is transmitted through multiple (air, bone and skin conduction) modes, as captured by the air, bone and throat microphones respectively. Speaker specific characteristics that capture this nonlinearity are rarely used as stand-alone features for speaker modeling, and at best have been used in tandem with well known linear spectral features to produce tangible results. This paper proposes Recurrent Plot (RP) embeddings as stand-alone, non-linear speaker-discriminating features. Two datasets, the continuous multimodal TIMIT speech corpus and the consonant-vowel unimodal syllable dataset, are used in this study for conducting closed-set speaker identification experiments. Experiments with unimodal speaker recognition systems show that RP embeddings capture the nonlinear dynamics of the VT system which are unique to every speaker, in all the modes of speech. The Air (A), Bone (B) and Throat (T) microphone systems, trained purely on RP embeddings perform with an accuracy of 95.81%, 98.18% and 99.74%, respectively. Experiments using the joint feature space of combined RP embeddings for bimodal (A-T, A-B, B-T) and trimodal (A-B-T) systems show that the best trimodal system (99.84% accuracy) performs on par with trimodal systems using spectrogram (99.45%) and MFCC (99.98%). The 98.84% performance of the B-T bimodal system shows the efficacy of a speaker recognition system based entirely on alternate (bone and throat) speech, in the absence of the standard (air) speech. The results underscore the significance of the RP embedding, as a nonlinear feature representation of the dynamical VT system that can act independently for speaker recognition. It is envisaged that speech recognition too will benefit from this nonlinear feature.

Interpersonal heart rate synchrony predicts effective information processing in a naturalistic group decision-making task

Groups often outperform individuals in problem-solving. Nevertheless, failure to critically evaluate ideas risks suboptimal outcomes through so-called groupthink. Prior studies have shown that people who hold shared goals, perspectives, or understanding of the environment show similar patterns of brain activity, which itself can be enhanced by consensus-building discussions. Whether shared arousal alone can predict collective decision-making outcomes, however, remains unknown. To address this gap, we computed interpersonal heart rate synchrony, a peripheral index of shared arousal associated with joint attention, empathic accuracy, and group cohesion, in 44 groups (n = 204) performing a collective decision-making task. The task required critical examination of all available information to override inferior, default options and make the right choice. Using multidimensional recurrence quantification analysis (MdRQA) and machine learning, we found that heart rate synchrony predicted the probability of groups reaching the correct consensus decision with >70% cross-validation accuracy-significantly higher than that predicted by the duration of discussions, subjective assessment of team function or baseline heart rates alone. We propose that heart rate synchrony during group discussion provides a biomarker of interpersonal engagement that facilitates adaptive learning and effective information sharing during collective decision-making.

Zooming into the Complex Dynamics of Electrodermal Activity Recorded during Emotional Stimuli: A Multiscale Approach

Physiological phenomena exhibit complex behaviours arising at multiple time scales. To investigate them, techniques derived from chaos theory were applied to physiological signals, providing promising results in distinguishing between healthy and pathological states. Fractal-like properties of electrodermal activity (EDA), a well-validated tool for monitoring the autonomic nervous system state, have been reported in previous literature. This study proposes the multiscale complexity index of electrodermal activity (MComEDA) to discern different autonomic responses based on EDA signals. This method builds upon our previously proposed algorithm, ComEDA, and it is empowered with a coarse-graining procedure to provide a view at multiple time scales of the EDA response. We tested MComEDA's performance on the EDA signals of two publicly available datasets, i.e., the Continuously Annotated Signals of Emotion (CASE) dataset and the Affect, Personality and Mood Research on Individuals and Groups (AMIGOS) dataset, both containing physiological data recorded from healthy participants during the view of ultra-short emotional video clips. Our results highlighted that the values of MComEDA were significantly different (p-value < 0.05 after Wilcoxon signed rank test with Bonferroni's correction) when comparing high- and low-arousal stimuli. Furthermore, MComEDA outperformed the single-scale approach in discriminating among different valence levels of high-arousal stimuli, e.g., showing significantly different values for scary and amusing stimuli (p-value = 0.024). These findings suggest that a multiscale approach to the nonlinear analysis of EDA signals can improve the information gathered on task-specific autonomic response, even when ultra-short time series are considered.

A novel multi-task machine learning classifier for rare disease patterning using cardiac strain imaging data

To provide accurate predictions, current machine learning-based solutions require large, manually labeled training datasets. We implement persistent homology (PH), a topological tool for studying the pattern of data, to analyze echocardiography-based strain data and differentiate between rare diseases like constrictive pericarditis (CP) and restrictive cardiomyopathy (RCM). Patient population (retrospectively registered) included those presenting with heart failure due to CP (n = 51), RCM (n = 47), and patients without heart failure symptoms (n = 53). Longitudinal, radial, and circumferential strains/strain rates for left ventricular segments were processed into topological feature vectors using Machine learning PH workflow. In differentiating CP and RCM, the PH workflow model had a ROC AUC of 0.94 (Sensitivity = 92%, Specificity = 81%), compared with the GLS model AUC of 0.69 (Sensitivity = 65%, Specificity = 66%). In differentiating between all three conditions, the PH workflow model had an AUC of 0.83 (Sensitivity = 68%, Specificity = 84%), compared with the GLS model AUC of 0.68 (Sensitivity = 52% and Specificity = 76%). By employing persistent homology to differentiate the "pattern" of cardiac deformations, our machine-learning approach provides reasonable accuracy when evaluating small datasets and aids in understanding and visualizing patterns of cardiac imaging data in clinically challenging disease states.

Robust inference of causality in high-dimensional dynamical processes from the Information Imbalance of distance ranks

We introduce an approach which allows detecting causal relationships between variables for which the time evolution is available. Causality is assessed by a variational scheme based on the Information Imbalance of distance ranks, a statistical test capable of inferring the relative information content of different distance measures. We test whether the predictability of a putative driven system Y can be improved by incorporating information from a potential driver system X, without explicitly modeling the underlying dynamics and without the need to compute probability densities of the dynamic variables. This framework makes causality detection possible even between high-dimensional systems where only few of the variables are known or measured. Benchmark tests on coupled chaotic dynamical systems demonstrate that our approach outperforms other model-free causality detection methods, successfully handling both unidirectional and bidirectional couplings. We also show that the method can be used to robustly detect causality in human electroencephalography data.

Reliable automatic sleep stage classification based on hybrid intelligence

Sleep staging is a vital aspect of sleep assessment, serving as a critical tool for evaluating the quality of sleep and identifying sleep disorders. Manual sleep staging is a laborious process, while automatic sleep staging is seldom utilized in clinical practice due to issues related to the inadequate accuracy and interpretability of classification results in automatic sleep staging models. In this work, a hybrid intelligent model is presented for automatic sleep staging, which integrates data intelligence and knowledge intelligence, to attain a balance between accuracy, interpretability, and generalizability in the sleep stage classification. Specifically, it is built on any combination of typical electroencephalography (EEG) and electrooculography (EOG) channels, including a temporal fully convolutional network based on the U-Net architecture and a multi-task feature mapping structure. The experimental results show that, compared to current interpretable automatic sleep staging models, our model achieves a Macro-F1 score of 0.804 on the ISRUC dataset and 0.780 on the Sleep-EDFx dataset. Moreover, we use knowledge intelligence to address issues of excessive jumps and unreasonable sleep stage transitions in the coarse sleep graphs obtained by the model. We also explore the different ways knowledge intelligence affects coarse sleep graphs by combining different sleep graph correction methods. Our research can offer convenient support for sleep physicians, indicating its significant potential in improving the efficiency of clinical sleep staging.

Resolving heterogeneity in dynamics of synchronization stability within the salience network in autism spectrum disorder

BACKGROUND

Heterogeneity in resting-state functional connectivity (FC) are one of the characteristics of autism spectrum disorder (ASD). Traditional resting-state FC primarily focuses on linear correlations, ignoring the nonlinear properties involved in synchronization between networks or brain regions.

METHODS

In the present study, the cross-recurrence quantification analysis, a nonlinear method based on dynamical systems, was utilized to quantify the synchronization stability between brain regions within the salience network (SN) of ASD. Using the resting-state functional magnetic resonance imaging data of 207 children (ASD/typically-developing controls (TC): 105/102) in Autism Brain Imaging Data Exchange database, we analyzed the laminarity and trapping time differences of the synchronization stability between the ASD subtype derived by a K-means clustering analysis and the TC group, and examined the relationship between synchronization stability and the severity of clinical symptoms of the ASD subtypes.

RESULTS

Based on the synchronization stability within the SN of ASD, we identified two subtypes that showed opposite changes in synchronization stability relative to the TC group. In addition, the synchronization stability of ASD subtypes 1 and 2 can predict the social interaction and communication impairments, respectively.

CONCLUSIONS

These findings reveal that ASD subgroups with different patterns of synchronization stability within the SN appear distinct clinical symptoms, and highlight the importance of exploring the potential neural mechanism of ASD from a nonlinear perspective.

Distinction of Chaos from Randomness Is Not Possible from the Degree Distribution of the Visibility and Phase Space Reconstruction Graphs

We investigate whether it is possible to distinguish chaotic time series from random time series using network theory. In this perspective, we selected four methods to generate graphs from time series: the natural, the horizontal, the limited penetrable horizontal visibility graph, and the phase space reconstruction method. These methods claim that the distinction of chaos from randomness is possible by studying the degree distribution of the generated graphs. We evaluated these methods by computing the results for chaotic time series from the 2D Torus Automorphisms, the chaotic Lorenz system, and a random sequence derived from the normal distribution. Although the results confirm previous studies, we found that the distinction of chaos from randomness is not generally possible in the context of the above methodologies.