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

Revealing causality in the associations between meteorological variables and air pollutant concentrations

Understanding the role of meteorology in determining air pollutant concentrations is an important goal for better comprehension of air pollution dispersion and fate. It requires estimating the strength of the causal associations between all the relevant meteorological variables and the pollutant concentrations. Unfortunately, many of the meteorological variables are not routinely observed. Furthermore, the common analysis methods cannot establish causality. Here we use the output of a numerical weather prediction model as a proxy for real meteorological data, and study the causal relationships between a large suite of its meteorological variables, including some rarely observed ones, and the corresponding nitrogen dioxide (NO2) concentrations at multiple observation locations. Time-lagged convergent cross mapping analysis is used to ascertain causality and its strength, and the Pearson and Spearman correlations are used to study the direction of the associations. The solar radiation, temperature lapse rate, boundary layer height, horizontal wind speed and wind shear were found to be causally associated with the NO2 concentrations, with mean time lags of their maximal impact at -3, -1, -2 and -3 hours, respectively. The nature of the association with the vertical wind speed was found to be uncertain and region-dependent. No causal association was found with relative humidity, temperature and precipitation.

Tapping into the human spinal locomotor centres with transspinal stimulation

Human locomotion is controlled by spinal neuronal networks of similar properties, function, and organization to those described in animals. Transspinal stimulation affects the spinal locomotor networks and is used to improve standing and walking ability in paralyzed people. However, the function of locomotor centers during transspinal stimulation at different frequencies and intensities is not known. Here, we document the 3D joint kinematics and spatiotemporal gait characteristics during transspinal stimulation at 15, 30, and 50 Hz at sub-threshold and supra-threshold stimulation intensities. We document the temporal structure of gait patterns, dynamic stability of joint movements over stride-to-stride fluctuations, and limb coordination during walking at a self-selected speed in healthy subjects. We found that transspinal stimulation (1) affects the kinematics of the hip, knee, and ankle joints, (2) promotes a more stable coordination at the left ankle, (3) affects interlimb coordination of the thighs, and (4) intralimb coordination between thigh and foot, (5) promotes greater dynamic stability of the hips, (6) increases the persistence of fluctuations in step length variability, and lastly (7) affects mechanical walking stability. These results support that transspinal stimulation is an important neuromodulatory strategy that directly affects gait symmetry and dynamic stability. The conservation of main effects at different frequencies and intensities calls for systematic investigation of stimulation protocols for clinical applications.

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 sub-optimal 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 multi-dimensional recurrence quantification analysis (MdRQA) and machine learning, we found that heart rate synchrony predicted the probability of groups reaching the correct consensus decision with greater than 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.

Interpretable predictions of chaotic dynamical systems using dynamical system deep learning

Making accurate predictions of chaotic dynamical systems is an essential but challenging task with many practical applications in various disciplines. However, the current dynamical methods can only provide short-term precise predictions, while prevailing deep learning techniques with better performances always suffer from model complexity and interpretability. Here, we propose a new dynamic-based deep learning method, namely the dynamical system deep learning (DSDL), to achieve interpretable long-term precise predictions by the combination of nonlinear dynamics theory and deep learning methods. As validated by four chaotic dynamical systems with different complexities, the DSDL framework significantly outperforms other dynamical and deep learning methods. Furthermore, the DSDL also reduces the model complexity and realizes the model transparency to make it more interpretable. We firmly believe that the DSDL framework is a promising and effective method for comprehending and predicting chaotic dynamical systems.

Exploring how metronome pacing at varying movement speeds influences local dynamic stability and coordination variability of lumbar spine motion during repetitive lifting

Auditory metronomes have been used to preserve movement consistency when examining local dynamic stability (LDS) and coordination variability (CV) of lumbar spine motion during repetitive movements. However, the potential influence of the metronome itself on these outcome measures has rarely been considered. Therefore, this study investigated the influence of different metronome paces (i.e., lifting speeds) on measures of lumbar spine LDS and thorax-pelvis CV during a repetitive lifting/lowering task in comparison to self-paced movements. Ten participants completed 5 repetitive lift/lower trials, where participants completed 35 consecutive repetitions (analysis on last 30 repetitions) at a self-selected pace for the first and last trial, and were paced by a 10 lift/min, 15 lift/min, and 20 lift/min metronome, in randomized order, for the remaining three trials. The average self-paced lift/lower speed before and after experiencing the three different metronome paced speeds was 16.2 (±1.02) and 17.2 (±0.73) lifts/min, respectively, and the most-preferred metronome pace trial was 15 lifts/min. Thorax-pelvis CV during the self-paced trials were similar (p > 0.05) to the 15 lift/min metronome paced trials, while greater thorax-pelvis CV was observed for the 10 lift/min compared to the 15 lift/min and 20 lift/min and second self-paced trial (all p < 0.026). This movement speed effect was not observed for lumbar spine LDS; however, more-dynamically stable movements were observed during all metronome paced trials in comparison to the self-paced trials. This study highlights that careful consideration is required when employing a metronome to control/manipulate movement characteristics while examining neuromuscular control using non-linear dynamical systems measures.

Exploring recurrence quantification analysis and fractal dimension algorithms for diagnosis of encephalopathy

Electroencephalography (EEG) is a crucial non-invasive medical tool for diagnosing neurological disorder called encephalopathy. There is a requirement for powerful signal processing algorithms as EEG patterns in encephalopathies are not specific to a particular etiology. As visual examination and linear methods of EEG analysis are not sufficient to get the subtle information regarding various neuro pathologies, non-linear analysis methods can be employed for exploring the dynamic, complex and chaotic nature of EEG signals. This work aims identifying and differentiating the patterns specific to cerebral dysfunctions associated with Encephalopathy using Recurrence Quantification Analysis and Fractal Dimension algorithms. This study analysed six RQA features, namely, recurrence rate, determinism, laminarity, diagonal length, diagonal entropy and trapping time and comparing them with fractal dimensions, namely, Higuchi's and Katz's fractal dimension. Fractal dimensions were found to be lower for encephalopathy cases showing decreased complexity when compared to that of normal healthy subjects. On the other hand, RQA features were found to be higher for encephalopathy cases indicating higher recurrence and more periodic patterns in EEGs of encephalopathy compared to that of normal healthy controls. The feature reduction was then performed using Principal Component Analysis and fed to three promising classifiers: SVM, Random Forest and Multi-layer Perceptron. The resultant system provides a practically realizable pipeline for the diagnosis of encephalopathy.

Correlation dimension of high-dimensional and high-definition experimental time series

The correlation dimension (CD) is a nonlinear measure of the complexity of invariant sets. First introduced for describing low-dimensional chaotic attractors, it has been later extended to the analysis of experimental electroencephalographic (EEG), magnetoencephalographic (MEG), and local field potential (LFP) recordings. However, its direct application to high-dimensional (dozens of signals) and high-definition (kHz sampling rate) 2HD data revealed a controversy in the results. We show that the need for an exponentially long data sample is the main difficulty in dealing with 2HD data. Then, we provide a novel method for estimating CD that enables orders of magnitude reduction of the required sample size. The approach decomposes raw data into statistically independent components and estimates the CD for each of them separately. In addition, the method allows ongoing insights into the interplay between the complexity of the contributing components, which can be related to different anatomical pathways and brain regions. The latter opens new approaches to a deeper interpretation of experimental data. Finally, we illustrate the method with synthetic data and LFPs recorded in the hippocampus of a rat.

Effects of trunk extensor muscle fatigue on repetitive lift (re)training using an augmented tactile feedback approach

Augmented tactile and performance feedback has been used to (re)train a modified lifting technique to reduce lumbar spine flexion, which has been associated with low back disorder development during occupational repetitive lifting tasks. However, it remains unknown if the presence of trunk extensor neuromuscular fatigue influences learning of this modified lifting technique. Therefore, we compared the effectiveness of using augmented tactile and performance feedback to reduce lumbar spine flexion during a repetitive lifting task, in both unfatigued and fatigued states. Participants completed repetitive lifting tests immediately before and after training, and 1-week later, with half of the participants completing training after fatiguing their trunk extensor muscles. Both groups demonstrated learning of the modified lifting technique as demonstrated by increased thorax-pelvis coordination variability and reduced lumbar range of motion variability; however, experiencing trunk extensor neuromuscular fatigue during lift (re)training may have slight negative influences on learning the modified lifting technique. Practitioner summary: An augmented lift (re)training paradigm using tactile cueing and performance feedback regarding key movement features (i.e. lumbar spine flexion) can effectively (re)train a modified lifting technique to reduce lumbar flexion and redistribute motion to the hips and knees. However, performing (re)training while fatigued could slightly hinder learning this lifting technique.

Measuring Prosodic Entrainment in Conversation: A Review and Comparison of Different Methods

PURPOSE

This study aims to further our understanding of prosodic entrainment and its different subtypes by analyzing a single corpus of conversations with 12 different methods and comparing the subsequent results.

METHOD

Entrainment on three fundamental frequency features was analyzed in a subset of recordings from the LUCID corpus (Baker & Hazan, 2011) using the following methods: global proximity, global convergence, local proximity, local convergence, local synchrony (Levitan & Hirschberg, 2011), prediction using linear mixed-effects models (Schweitzer & Lewandowski, 2013), geometric approach (Lehnert-LeHouillier, Terrazas, & Sandoval, 2020), time-aligned moving average (Kousidis et al., 2008), HYBRID method (De Looze et al., 2014), cross-recurrence quantification analysis (e.g., Fusaroli & Tylén, 2016), and windowed, lagged cross-correlation (Boker et al., 2002). We employed entrainment measures on a local timescale (i.e., on adjacent utterances), a global timescale (i.e., over larger time frames), and a time series-based timescale that is larger than adjacent utterances but smaller than entire conversations.

RESULTS

We observed variance in results of different methods.

CONCLUSIONS

Results suggest that each method may measure a slightly different type of entrainment. The complex implications this has for existing and future research are discussed.

Trunk variability and local dynamic stability during gait after generalized fatigue induced by incremental exercise test in young women in different phases of the menstrual cycle

Purpose

The purpose of this study was to identify how generalized fatigue along with hormonal changes throughout the menstrual cycle affects trunk variability and local dynamic stability during gait.

Methods

General fatigue was induced by an incremental test on a treadmill, and the menstrual cycle was divided into three phases: follicular, ovulatory, and luteal. Twenty-six healthy, young volunteers (aged 18 to 28 years) who did not use oral contraceptives or other hormonal drugs with a regular menstrual cycle participated in the study. They walked on the treadmill for 4 min at the preferred speed, before the incremental test, followed by four sets of 4 min alternating between walking, also at preferred speed, and resting. From trunk kinematic data, the following were extracted: the mean of the standard deviation along strides, as a measure of variability, and the maximum Lyapunov exponent, as a measure of local dynamic stability (LDS).

Results

After the incremental test, variability increased, and LDS decreased. However, they showed a tendency to return to the initial value faster in women compared to previous results for men. In the follicular phase, which has less hormonal release, the volunteers had an almost complete recovery in LDS soon after the first rest interval, suggesting that female hormones can interfere with fatigue recovery. Nevertheless, concerning the LDS, it was significantly lower in the luteal phase than in the follicular phase.

Conclusion

Women that are not taking oral contraceptives should be aware that they are susceptible to increased gait instabilities in the pre-menstrual phase after strenuous activities.

Unraveling dyadic psycho-physiology of social presence between strangers during an audio drama - a signal-analysis approach

A mere co-presence of an unfamiliar person may modulate an individual's attentive engagement with specific events or situations to a significant degree. To understand better how such social presence affects experiences, we recorded a set of parallel multimodal facial and psychophysiological data with subjects (N = 36) who listened to dramatic audio scenes alone or when facing an unfamiliar person. Both a selection of 6 s affective sound clips (IADS-2) followed by a 27 min soundtrack extracted from a Finnish episode film depicted familiar and often intense social situations familiar from the everyday world. Considering the systemic complexity of both the chosen naturalistic stimuli and expected variations in the experimental social situation, we applied a novel combination of signal analysis methods using inter-subject correlation (ISC) analysis, Representational Similarity Analysis (RSA) and Recurrence Quantification Analysis (RQA) followed by gradient boosting classification. We report our findings concerning three facial signals, gaze, eyebrow and smile that can be linked to socially motivated facial movements. We found that ISC values of pairs, whether calculated on true pairs or any two individuals who had a partner, were lower than the group with single individuals. Thus, audio stimuli induced more unique responses in those subjects who were listening to it in the presence of another person, while individual listeners tended to yield a more uniform response as it was driven by dramatized audio stimulus alone. Furthermore, our classifiers models trained using recurrence properties of gaze, eyebrows and smile signals demonstrated distinctive differences in the recurrence dynamics of signals from paired subjects and revealed the impact of individual differences on the latter. We showed that the presence of an unfamiliar co-listener that modifies social dynamics of dyadic listening tasks can be detected reliably from visible facial modalities. By applying our analysis framework to a broader range of psycho-physiological data, together with annotations of the content, and subjective reports of participants, we expected more detailed dyadic dependencies to be revealed. Our work contributes towards modeling and predicting human social behaviors to specific types of audio-visually mediated, virtual, and live social situations.

A Symmetrized Dot Pattern Extraction Method Based on Frobenius and Nuclear Hybrid Norm Penalized Robust Principal Component Analysis and Decomposition and Reconstruction

Due to their symmetrized dot pattern, rolling bearings are more susceptible to noise than time-frequency characteristics. Therefore, this article proposes a symmetrized dot pattern extraction method based on the Frobenius and nuclear hybrid norm penalized robust principal component analysis (FNHN-RPCA) as well as decomposition and reconstruction. This method focuses on denoising the vibration signal before calculating the symmetric dot pattern. Firstly, the FNHN-RPCA is used to remove the non-correlation between variables to realize the separation of feature information and interference noise. After, the residual interference noise, irrelevant information, and fault features in the separated signal are clearly located in different frequency bands. Then, the ensemble empirical mode decomposition is applied to decompose this information into different intrinsic mode function components, and the improved DPR/KLdiv criterion is used to select components containing fault features for reconstruction. In addition, the symmetrized dot pattern is used to visualize the reconstructed signal. Finally, method validation and comparative analysis are conducted on the CWRU datasets and experimental bench data, respectively. The results show that the improved criteria can accurately complete the screening task, and the proposed method can effectively reduce the impact of strong noise interference on SDPs.

Multichannel measurements of C. elegans largest Lyapunov exponents using optical diffraction

Dynamic diffraction (DOD) is a form of microscopy that allows the dynamic tracking of changing shapes in a 1D time series. DOD can capture the locomotion of a nematode while swimming freely in a 3D space, allowing the locomotion of the worm to more closely mimic natural behavior than in some other laboratory environments. More importantly, we are able to see markers of chaos as DOD covers dynamics on multiple length scales. This work introduces a multichannel method to measure the dynamic complexity of microscopic organisms. We show that parameters associated with chaos, such as the largest Lyapunov exponent (LLE), the mean frequency, mutual information (MI), and the embedding dimension, are independent of the specific point sampled in the diffraction pattern, thus demonstrating experimentally the consistency of our dynamic parameters sampled at various locations (channels) in the associated optical far-field pattern.

Dynamical Analyses Show That Professional Archers Exhibit Tighter, Finer and More Fluid Dynamical Control Than Neophytes

Quantifying the dynamical features of discrete tasks is essential to understanding athletic performance for many sports that are not repetitive or cyclical. We compared three dynamical features of the (i) bow hand, (ii) drawing hand, and (iii) center of mass during a single bow-draw movement between professional and neophyte archers: dispersion (convex hull volume of their phase portraits), persistence (tendency to continue a trend as per Hurst exponents), and regularity (sample entropy). Although differences in the two groups are expected due to their differences in skill, our results demonstrate we can quantify these differences. The center of mass of professional athletes exhibits tighter movements compared to neophyte archers (6.3 < 11.2 convex hull volume), which are nevertheless less persistent (0.82 < 0.86 Hurst exponent) and less regular (0.035 > 0.025 sample entropy). In particular, the movements of the bow hand and center of mass differed more between groups in Hurst exponent analysis, and the drawing hand and center of mass were more different in sample entropy analysis. This suggests tighter neuromuscular control over the more fluid dynamics of the movement that exhibits more active corrections that are more individualized. Our work, therefore, provides proof of principle of how well-established dynamical analysis techniques can be used to quantify the nature and features of neuromuscular expertise for discrete movements in elite athletes.

Multivariate joint order recurrence networks for characterization of multi-lead ECG time series from healthy and pathological heartbeat dynamics

Analysis of nonlinear dynamic characteristics of cardiac systems has been a hot topic of clinical research, and the recurrence plots have earned much attention as an effective tool for it. In this paper, we propose a novel method of multivariate joint order recurrence networks (MJORNs) to evaluate the multi-lead electrocardiography (ECG) time series with healthy and psychological heart states. The similarity between time series is studied by quantifying the structure in a joint order pattern recurrence plot. We take the time series that corresponds to each of the 12-lead ECG signals as a node in the network and use the entropy of diagonal line length that describes the complex structure of joint order pattern recurrence plot as the weight to construct MJORN. The analysis of network topology reveals differences in nonlinear complexity for healthy and heart diseased heartbeat systems. Experimental outcomes show that the values of average weighted path length are reduced in MJORN constructed from crowds with heart diseases, compared to those from healthy individuals, and the results of the average weighted clustering coefficient are the opposite. Due to the impaired cardiac fractal-like structures, the similarity between different leads of ECG is reduced, leading to a decrease in the nonlinear complexity of the cardiac system. The topological changes of MJORN reflect, to some extent, modifications in the nonlinear dynamics of the cardiac system from healthy to diseased conditions. Compared to multivariate cross recurrence networks and multivariate joint recurrence networks, our results suggest that MJORN performs better in discriminating healthy and pathological heartbeat dynamics.

A method of stall recognition using nonlinear feature extraction from the compressor outlet pressure

The paper presents a method for analysing the pressure signal at the compressor outlet, which allows to detect when the machine operating point approaches the area where a stall is about to occur. The signal analysis method is based on nonlinear feature extraction from the dynamic signal. The correlation dimension (d corr ) is used to quantify the complexity of the measured signal, its value decreasing if the analysed signal originates from deterministic processes. The results presented indicate that the correlation dimension of the signal decreases at flow rates approximately 10% above the flow rate at which negative effects on machine performance occur. This trend has been observed across multiple rotor speeds. These findings suggest that the perturbations associated with the onset of the stall can propagate to the compressor outlet, leading to less chaotic pressure behaviour that reflects the dynamics of these perturbations. The fact that stall can be identified from the pressure signal in the space between the rotor and the diffuser in its early stages is well known, but the possibility of identifying stall at the compressor outlet, where the perturbations are significantly attenuated, has not been documented in the literature.

An adaptive embedding procedure for time series forecasting with deep neural networks

Nowadays, solving time series prediction problems is an open and challenging task. Many solutions are based on the implementation of deep neural architectures, which are able to analyze the structure of the time series and to carry out the prediction. In this work, we present a novel deep learning scheme based on an adaptive embedding mechanism. The latter is exploited to extract a compressed representation of the input time series that is used for the subsequent forecasting. The proposed model is based on a two-layer bidirectional Long Short-Term Memory network, where the first layer performs the adaptive embedding and the second layer acts as a predictor. The performances of the proposed forecasting scheme are compared with several models in two different scenarios, considering both well-known time series and real-life application cases. The experimental results show the accuracy and the flexibility of the proposed approach, which can be used as a prediction tool for any actual application.

A Mechanical Defect Localization and Identification Method for High-Voltage Circuit Breakers Based on the Segmentation of Vibration Signals and Extraction of Chaotic Features

To address the problem of mechanical defect identification in a high-voltage circuit breaker (HVCB), this paper studies the circuit breaker vibration signal and proposes a method of feature extraction based on phase-space reconstruction of the vibration substages. To locate mechanical defects in circuit breakers, vibration signals are divided into different substages according to the time sequence of the parts of the circuit breakers. The largest Lyapunov exponent (LLE) of the vibration signals' substages is calculated, and then the substages are reconstructed in high-dimensional phase space. The geometric features of the phase trajectory mean center distance (MCD) and vector diameter offset (VDO) are calculated, and the LLE, MCD, and VDO are selected as the three fault identification features of the vibration substages. The eigenvalue anomaly rate of each substage of the vibration signal under defect state are calculated and analyzed to locate the vibration substage of the mechanical defect. Finally, a fault diagnosis model is constructed by a support vector machine (SVM), and the common mechanical defects of circuit breakers simulated in the laboratory are effectively identified.

Optical transmitter fingerprint construction and identification based on chaotic phase space reconfiguration

An optical transmitter identification scheme based on optical chaotic phase space reconfiguration for secure communication is proposed to target injection attacks in the physical layer of optical networks. First, a feature fingerprint construction method based on reconfigured phase space of optical chaos is proposed. Then the fingerprint is controlled by the feedback intensity and filtering bandwidth of chaos. The in-phase and quadrature-phase encryption (IQE)/decryption (IQD) ensures the loading of fingerprints and realizes the confidential communication. In the experiment, the recognition rate of three transmitters is up to 99.3%. In the simulation, the recognition rate of five optical transmitters reaches 100% after 600 km transmission. The bit error rate of 25 GBaud QPSK signal after 300 km transmission at 25 dB OSNR is 1.6 × 10-3. Compared with the traditional optical transmitter identification methods, the fingerprint of this scheme is controllable. The IQE and IQD not only realize the chaotic fingerprint loading but also ensure the secure transmission of the signal avoiding the synchronization and time delay exposure problems in traditional chaotic communication systems. It is robust to device parameters, with low implementation difficulty and low cost. Therefore, this scheme has research and application value for secure communication in the physical layer of optical networks.

Dynamic state of low-Reynolds-number turbulent channel flow

We numerically study the dynamic state of a low-Reynolds-number turbulent channel flow from the viewpoints of symbolic dynamics and nonlinear forecasting. A low-dimensionally (high-dimensionally) chaotic state of the streamwise velocity fluctuations emerges at a viscous sublayer (logarithmic layer). The possible presence of the chaotic states is clearly identified by orbital instability-based nonlinear forecasting and ordinal partition transition network entropy in combination with the surrogate data method.

Recurrence quantification analysis of postural sway in patients with persistent postural perceptual dizziness

Background

Persistent postural perceptual dizziness (PPPD) is a common cause of chronic dizziness and imbalance. Emerging evidence suggests that changes in quantitative measures of postural control may help identify individuals with PPPD, however, traditional linear metrics of sway have yielded inconsistent results. Methodologies to examine the temporal structure of sway, including recurrent quantification analysis (RQA), have identified unique changes in dynamic structure of postural control in other patient populations. This study aimed to determine if adults with PPPD exhibit changes in the dynamic structure of sway and whether this change is modulated on the basis of available sensory cues.

Methods

Twelve adults diagnosed with PPPD and twelve age-matched controls, completed a standard battery of quiet stance balance tasks that involved the manipulation of visual and/or proprioceptive feedback. For each group, the regularity and complexity of the CoP signal was assessed using RQA and the magnitude and variability of the CoP signal was quantified using traditional linear measures.

Results

An overall effect of participant group (i.e., healthy controls vs. PPPD) was seen for non-linear measures of temporal complexity quantified using RQA. Changes in determinism (i.e., regularity) were also modulated on the basis of availability of sensory cues in patients with PPPD. No between-group difference was identified for linear measures assessing amount and variability of sway.

Conclusions

Participants with PPPD on average exhibited sway that was similar in magnitude to, but significantly more repeatable and less complex than, healthy controls. These data show that non-linear measures provide unique information regarding the effect of PPPD on postural control, and as a result, may serve as potential rehabilitation outcome measures.

Excellent predictive-performances of photonic reservoir computers for chaotic time-series using the fusion-prediction approach

In this work, based on two parallel reservoir computers realized by the two polarization components of the optically pumped spin-VCSEL with double optical feedbacks, we propose the fusion-prediction scheme for the Mackey-Glass (MG) and Lorenz (LZ) chaotic time series. Here, the direct prediction and iterative prediction results are fused in a weighted average way. Compared with the direct-prediction errors, the fusion-prediction errors appear great decrease. Their values are far less than the values of the direct-prediction errors when the iteration step-size are no more than 15. By the optimization of the temporal interval and the sampling period, under the iteration step-size of 3, the fusion-prediction errors for the MG and LZ chaotic time-series can be reduced to 0.00178 and 0.004627, which become 8.1% of the corresponding direct-prediction error and 28.68% of one, respectively. Even though the iteration step-size reaches to 15, the fusion-prediction errors for the MG and LZ chaotic time-series can be reduced to 55.61% of the corresponding direct-prediction error and 77.28% of one, respectively. In addition, the fusion-prediction errors have strong robustness on the perturbations of the system parameters. Our studied results can potentially apply in the improvement of prediction accuracy for some complex nonlinear time series.

Autonomic Regulation of Facial Temperature during Stress: A Cross-Mapping Analysis

Skin temperature reflects the Autonomic Nervous System (ANS)'s response to emotions and mental states and can be remotely measured using InfraRed Thermography. Understanding the physiological mechanisms that affect facial temperature is essential to improve the precision of emotional inference from thermal imaging. To achieve this aim, we recorded thermal images from 30 volunteers, at rest and under acute stress induced by the Stroop test, together with two autonomic correlates, i.e., heart rate variability and electrodermal activity, the former serving as a measure of cardiovascular dynamics, and the latter of the activity of the sweat glands. We used a Cross Mapping (CM) approach to quantify the nonlinear coupling of the temperature from four facial regions with the ANS correlates. CM reveals that facial temperature has a statistically significant correlation with the two autonomic time series, under both conditions, which was not evident in the linear domain. In particular, compared to the other regions, the nose shows a significantly higher link to the electrodermal activity in both conditions, and to the heart rate variability under stress. Moreover, the cardiovascular activity seems to be primarily responsible for the well-known decrease in nose temperature, and its coupling with the thermal signals significantly varies with gender.

A Dynamical Systems Approach to Characterizing Brain-Body Interactions during Movement: Challenges, Interpretations, and Recommendations

Brain-body interactions (BBIs) have been the focus of intense scrutiny since the inception of the scientific method, playing a foundational role in the earliest debates over the philosophy of science. Contemporary investigations of BBIs to elucidate the neural principles of motor control have benefited from advances in neuroimaging, device engineering, and signal processing. However, these studies generally suffer from two major limitations. First, they rely on interpretations of 'brain' activity that are behavioral in nature, rather than neuroanatomical or biophysical. Second, they employ methodological approaches that are inconsistent with a dynamical systems approach to neuromotor control. These limitations represent a fundamental challenge to the use of BBIs for answering basic and applied research questions in neuroimaging and neurorehabilitation. Thus, this review is written as a tutorial to address both limitations for those interested in studying BBIs through a dynamical systems lens. First, we outline current best practices for acquiring, interpreting, and cleaning scalp-measured electroencephalography (EEG) acquired during whole-body movement. Second, we discuss historical and current theories for modeling EEG and kinematic data as dynamical systems. Third, we provide worked examples from both canonical model systems and from empirical EEG and kinematic data collected from two subjects during an overground walking task.

Two-channel EEG based diagnosis of panic disorder and major depressive disorder using machine learning and non-linear dynamical methods

The current study aimed to investigate the possibility of rapid and accurate diagnoses of Panic disorder (PD) and Major depressive disorder (MDD) using machine learning. The support vector machine method was applied to 2-channel EEG signals from the frontal lobes (Fp1 and Fp2) of 149 participants to classify PD and MDD patients from healthy individuals using non-linear measures as features. We found significantly lower correlation dimension and Lempel-Ziv complexity in PD patients and MDD patients in the left hemisphere compared to healthy subjects at rest. Most importantly, we obtained a 90% accuracy in classifying MDD patients vs. healthy individuals, a 68% accuracy in classifying PD patients vs. controls, and a 59% classification accuracy between PD and MDD patients. In addition to demonstrating classification performance in a simplified setting, the observed differences in EEG complexity between subject groups suggest altered cortical processing present in the frontal lobes of PD patients that can be captured through non-linear measures. Overall, this study suggests that machine learning and non-linear measures using only 2-channel frontal EEGs are useful for aiding the rapid diagnosis of panic disorder and major depressive disorder.

Multilayer Perceptron Network Optimization for Chaotic Time Series Modeling

Chaotic time series are widely present in practice, but due to their characteristics-such as internal randomness, nonlinearity, and long-term unpredictability-it is difficult to achieve high-precision intermediate or long-term predictions. Multi-layer perceptron (MLP) networks are an effective tool for chaotic time series modeling. Focusing on chaotic time series modeling, this paper presents a generalized degree of freedom approximation method of MLP. We then obtain its Akachi information criterion, which is designed as the loss function for training, hence developing an overall framework for chaotic time series analysis, including phase space reconstruction, model training, and model selection. To verify the effectiveness of the proposed method, it is applied to two artificial chaotic time series and two real-world chaotic time series. The numerical results show that the proposed optimized method is effective to obtain the best model from a group of candidates. Moreover, the optimized models perform very well in multi-step prediction tasks.

Interconnected ordinal pattern complex network for characterizing the spatial coupling behavior of gas-liquid two-phase flow

The complex phase interactions of the two-phase flow are a key factor in understanding the flow pattern evolutional mechanisms, yet these complex flow behaviors have not been well understood. In this paper, we employ a series of gas-liquid two-phase flow multivariate fluctuation signals as observations and propose a novel interconnected ordinal pattern network to investigate the spatial coupling behaviors of the gas-liquid two-phase flow patterns. In addition, we use two network indices, which are the global subnetwork mutual information (I) and the global subnetwork clustering coefficient (C), to quantitatively measure the spatial coupling strength of different gas-liquid flow patterns. The gas-liquid two-phase flow pattern evolutionary behaviors are further characterized by calculating the two proposed coupling indices under different flow conditions. The proposed interconnected ordinal pattern network provides a novel tool for a deeper understanding of the evolutional mechanisms of the multi-phase flow system, and it can also be used to investigate the coupling behaviors of other complex systems with multiple observations.

Recurrence quantification analysis during a mental calculation task

The identification of brain dynamical changes under different cognitive conditions with noninvasive techniques such as electroencephalography (EEG) is relevant for the understanding of their underlying neural mechanisms. The comprehension of these mechanisms has applications in the early diagnosis of neurological disorders and asynchronous brain computer interfaces. In both cases, there are no reported features that could describe intersubject and intra subject dynamics behavior accurately enough to be applied on a daily basis. The present work proposes the use of three nonlinear features (recurrence rate, determinism, and recurrence times) extracted from recurrence quantification analysis (RQA) to describe central and parietal EEG power series complexity in continuous alternating episodes of mental calculation and rest state. Our results demonstrate a consistent mean directional change of determinism, recurrence rate, and recurrence times between conditions. Increasing values of determinism and recurrence rate were present from the rest state to mental calculation, whereas recurrence times showed the opposite pattern. The analyzed features in the present study showed statistically significant changes between rest and mental calculation states in both individual and population analysis. In general, our study described mental calculation EEG power series as less complex systems in comparison to the rest state. Moreover, ANOVA showed stability of RQA features along time.

Analysis of Movement Variability in Cycling: An Exploratory Study

The purpose of this study was to determine the test-retest repeatability of Blue Trident inertial measurement units (IMUs) and VICON Nexus kinematic modelling in analysing the Lyapunov Exponent (LyE) during a maximal effort 4000 m cycling bout in different body segments/joints. An additional aim was to determine if changes in the LyE existed across a trial. Twelve novice cyclists completed four sessions of cycling; one was a familiarisation session to determine a bike fit and become better accustomed to the time trial position and pacing of a 4000 m effort. IMUs were attached to the head, thorax, pelvis and left and right shanks to analyse segment accelerations, respectively, and reflective markers were attached to the participant to analyse neck, thorax, pelvis, hip, knee and ankle segment/joint angular kinematics, respectively. Both the IMU and VICON Nexus test-retest repeatability ranged from poor to excellent at the different sites. In each session, the head and thorax IMU acceleration LyE increased across the bout, whilst pelvic and shank acceleration remained consistent. Differences across sessions were evident in VICON Nexus segment/joint angular kinematics, but no consistent trend existed. The improved reliability and the ability to identify a consistent trend in performance, combined with their improved portability and reduced cost, advocate for the use of IMUs in analysing movement variability in cycling. However, additional research is required to determine the applicability of analysing movement variability during cycling.

Fingerprint construction of optical transmitters based on the characteristic of electro-optic chaos for secure authentication

In this paper, an optical transmitter authentication method using hardware fingerprints based on the characteristic of electro-optic chaos is proposed. By means of phase space reconstruction of chaotic time series generated by an electro-optic feedback loop, the largest Lyapunov exponent spectrum (LLES) is defined and used as the hardware fingerprint for secure authentication. The time division multiplexing (TDM) module and the optical temporal encryption (OTE) module are introduced to combine chaotic signal and the message to ensure the security of the fingerprint. Support vector machine (SVM) models are trained to recognize legal and illegal optical transmitters at the receiver. Simulation results show that LLES of chaos has the fingerprint characteristic and is highly sensitive to the time delay of the electro-optic feedback loop. The trained SVM models can distinguish electro-optic chaos generated by different feedback loops with a time delay difference of only 0.03ns and have a good anti-noise ability. Experimental results show that the recognition accuracy of the authentication module based on LLES can reach 98.20% for both legal and illegal transmitters. Our strategy can improve the defense ability of optical networks against active injection attacks and has high flexibility.

Morphodynamical cell state description via live-cell imaging trajectory embedding

Time-lapse imaging is a powerful approach to gain insight into the dynamic responses of cells, but the quantitative analysis of morphological changes over time remains challenging. Here, we exploit the concept of "trajectory embedding" to analyze cellular behavior using morphological feature trajectory histories-that is, multiple time points simultaneously, rather than the more common practice of examining morphological feature time courses in single timepoint (snapshot) morphological features. We apply this approach to analyze live-cell images of MCF10A mammary epithelial cells after treatment with a panel of microenvironmental perturbagens that strongly modulate cell motility, morphology, and cell cycle behavior. Our morphodynamical trajectory embedding analysis constructs a shared cell state landscape revealing ligand-specific regulation of cell state transitions and enables quantitative and descriptive models of single-cell trajectories. Additionally, we show that incorporation of trajectories into single-cell morphological analysis enables (i) systematic characterization of cell state trajectories, (ii) better separation of phenotypes, and (iii) more descriptive models of ligand-induced differences as compared to snapshot-based analysis. This morphodynamical trajectory embedding is broadly applicable to the quantitative analysis of cell responses via live-cell imaging across many biological and biomedical applications.

Microscale Neuronal Activity Collectively Drives Chaotic and Inflexible Dynamics at the Macroscale in Seizures

Neuronal activity propagates through the network during seizures, engaging brain dynamics at multiple scales. Such propagating events can be described through the avalanches framework, which can relate spatiotemporal activity at the microscale with global network properties. Interestingly, propagating avalanches in healthy networks are indicative of critical dynamics, where the network is organized to a phase transition, which optimizes certain computational properties. Some have hypothesized that the pathologic brain dynamics of epileptic seizures are an emergent property of microscale neuronal networks collectively driving the brain away from criticality. Demonstrating this would provide a unifying mechanism linking microscale spatiotemporal activity with emergent brain dysfunction during seizures. Here, we investigated the effect of drug-induced seizures on critical avalanche dynamics, using in vivo whole-brain two-photon imaging of GCaMP6s larval zebrafish (males and females) at single neuron resolution. We demonstrate that single neuron activity across the whole brain exhibits a loss of critical statistics during seizures, suggesting that microscale activity collectively drives macroscale dynamics away from criticality. We also construct spiking network models at the scale of the larval zebrafish brain, to demonstrate that only densely connected networks can drive brain-wide seizure dynamics away from criticality. Importantly, such dense networks also disrupt the optimal computational capacities of critical networks, leading to chaotic dynamics, impaired network response properties and sticky states, thus helping to explain functional impairments during seizures. This study bridges the gap between microscale neuronal activity and emergent macroscale dynamics and cognitive dysfunction during seizures.SIGNIFICANCE STATEMENT Epileptic seizures are debilitating and impair normal brain function. It is unclear how the coordinated behavior of neurons collectively impairs brain function during seizures. To investigate this we perform fluorescence microscopy in larval zebrafish, which allows for the recording of whole-brain activity at single-neuron resolution. Using techniques from physics, we show that neuronal activity during seizures drives the brain away from criticality, a regime that enables both high and low activity states, into an inflexible regime that drives high activity states. Importantly, this change is caused by more connections in the network, which we show disrupts the ability of the brain to respond appropriately to its environment. Therefore, we identify key neuronal network mechanisms driving seizures and concurrent cognitive dysfunction.

Combining Heart Rate Variability and Oximetry to Improve Apneic Event Screening in Non-Desaturating Patients

In this paper, we thoroughly analyze the detection of sleep apnea events in the context of Obstructive Sleep Apnea (OSA), which is considered a public health problem because of its high prevalence and serious health implications. We especially evaluate patients who do not always show desaturations during apneic episodes (non-desaturating patients). For this purpose, we use a database (HuGCDN2014-OXI) that includes desaturating and non-desaturating patients, and we use the widely used Physionet Apnea Dataset for a meaningful comparison with prior work. Our system combines features extracted from the Heart-Rate Variability (HRV) and SpO₂, and it explores their potential to characterize desaturating and non-desaturating events. The HRV-based features include spectral, cepstral, and nonlinear information (Detrended Fluctuation Analysis (DFA) and Recurrence Quantification Analysis (RQA)). SpO₂-based features include temporal (variance) and spectral information. The features feed a Linear Discriminant Analysis (LDA) classifier. The goal is to evaluate the effect of using these features either individually or in combination, especially in non-desaturating patients. The main results for the detection of apneic events are: (a) Physionet success rate of 96.19%, sensitivity of 95.74% and specificity of 95.25% (Area Under Curve (AUC): 0.99); (b) HuGCDN2014-OXI of 87.32%, 83.81% and 88.55% (AUC: 0.934), respectively. The best results for the global diagnosis of OSA patients (HuGCDN2014-OXI) are: success rate of 95.74%, sensitivity of 100%, and specificity of 89.47%. We conclude that combining both features is the most accurate option, especially when there are non-desaturating patterns among the recordings under study.

Joint behaviour during arm swing changes with gait speed and predicts spatiotemporal variability and dynamic stability in healthy young adults

BACKGROUND

Arm swing is linked to gait stability. How this is accomplished is unclear as most investigations artificially manipulate arm swing amplitude and examine average patterns. Biomechanical evaluation of stride-to-stride upper limb behaviour across a range of gait speeds, where the arm swings as preferred, could clarify this link.

RESEARCH QUESTION

How do stride-to-stride arm swing behaviours change with gait speed and relate to stride-to-stride gait fluctuations?

METHODS

Young adults (n = 45, 25 females) completed treadmill gait at preferred, slow (70% of preferred), and fast speed (130% of preferred) while full-body kinematics were acquired with optoelectronic motion capture. Arm swing behaviour was quantified by shoulder, elbow, and wrist joint angle amplitude (range of motion [ROM]) and motor variability (e.g. mean standard deviation [meanSD], local divergence exponent [λ_max]). Stride-to-stride gait fluctuation was quantified by spatiotemporal variability (e.g. stride time CV) and dynamic stability (i.e. trunk local dynamic stability [trunk λ_max], centre-of-mass smoothness [COM HR]). Repeated measures ANOVAs tested for speed effects and step-wise linear regressions identified arm swing-based predictors of stride-to-stride gait fluctuation.

RESULTS

Speed decreased spatiotemporal variability and increased trunk λ_max and COM HR in the anteroposterior and vertical axes. Adjustments in gait fluctuations occurred with increased upper limb ROM, particularly for elbow flexion, and increased meanSD and λ_max of shoulder, elbow, and wrist angles. Models of upper limb measures predicted 49.9-55.5% of spatiotemporal variability and 17.7-46.4% of dynamic stability. For dynamic stability, wrist angle features were the best and most common independent predictors.

SIGNIFICANCE

Findings highlight that all upper limb joints, and not solely the shoulder, underlie changes in arm swing amplitude, and that arm swing strategies pair with the trunk and contrast with centre-of-mass and stride strategies. Findings suggest that young adults search for flexible arm swing motor strategies to help optimize stride consistency and gait smoothness.

Nonlinear analysis of heart rate variability signals in meditative state: a review and perspective

INTRODUCTION

In recent times, an upsurge in the investigation related to the effects of meditation in reconditioning various cardiovascular and psychological disorders is seen. In majority of these studies, heart rate variability (HRV) signal is used, probably for its ease of acquisition and low cost. Although understanding the dynamical complexity of HRV is not an easy task, the advances in nonlinear analysis has significantly helped in analyzing the impact of meditation of heart regulations. In this review, we intend to present the various nonlinear approaches, scientific findings and their limitations to develop deeper insights to carry out further research on this topic.

RESULTS

Literature have shown that research focus on nonlinear domain is mainly concentrated on assessing predictability, fractality, and entropy-based dynamical complexity of HRV signal. Although there were some conflicting results, most of the studies observed a reduced dynamical complexity, reduced fractal dimension, and decimated long-range correlation behavior during meditation. However, techniques, such as multiscale entropy (MSE) and multifractal analysis (MFA) of HRV can be more effective in analyzing non-stationary HRV signal, which were hardly used in the existing research works on meditation.

CONCLUSIONS

After going through the literature, it is realized that there is a requirement of a more rigorous research to get consistent and new findings about the changes in HRV dynamics due to the practice of meditation. The lack of adequate standard open access database is a concern in drawing statistically reliable results. Albeit, data augmentation technique is an alternative option to deal with this problem, data from adequate number of subjects can be more effective. Multiscale entropy analysis is scantily employed in studying the effect of meditation, which probably need more attention along with multifractal analysis.

METHODS

Scientific databases, namely PubMed, Google Scholar, Web of Science, Scopus were searched to obtain the literature on "HRV analysis during meditation by nonlinear methods". Following an exclusion criteria, 26 articles were selected to carry out this scientific analysis.

Unravelling quantum chaos using persistent homology

Topological data analysis is a powerful framework for extracting useful topological information from complex data sets. Recent work has shown its application for the dynamical analysis of classical dissipative systems through a topology-preserving embedding method that allows reconstructing dynamical attractors, the topologies of which can be used to identify chaotic behavior. Open quantum systems can similarly exhibit nontrivial dynamics, but the existing toolkit for classification and quantification are still limited, particularly for experimental applications. In this paper, we present a topological pipeline for characterizing quantum dynamics, which draws inspiration from the classical approach by using single quantum trajectory unravelings of the master equation to construct analog quantum attractors and extract their topology using persistent homology. We apply the method to a periodically modulated Kerr-nonlinear cavity to discriminate parameter regimes of regular and chaotic phases using limited measurements of the system.

Recurrence quantification analysis of isokinetic strength tests: A comparison of the anterior cruciate ligament reconstructed and the uninjured limb

BACKGROUND

Despite widespread use of return to sport testing following anterior cruciate ligament reconstruction, studies suggest inadequacy in current testing criteria, such as limb symmetry index calculations, to determine athletes' readiness to return to play. Recurrence quantification analysis, an emerging non-linear data analysis tool, may reveal subtle neuromuscular differences between the injured and uninjured limb that are not captured by traditional testing. We hypothesized that isokinetic torque curve data of the injured limb would demonstrate lower determinism and entropy as compared to the uninjured limb.

METHODS

102 patients (44 M, 58F, 10 ± 1 months post-anterior cruciate ligament reconstruction) underwent isokinetic quadriceps strength testing using a HumacNorm dynamometer. Patients completed maximum effort knee extension and flexion at 60°/sec. Data were post-processed with a MATLAB CRQA Graphical User Interface and determinism and entropy values were extracted. Paired-sample t-tests (α = 0.05) were used to compare data from the injured and uninjured limb.

FINDINGS

Determinism and entropy values in the torque curves were lower in the injured limb than the uninjured limb (p < 0.001). Our findings indicate there is less predictability and complexity present in the torque signals of injured limbs.

INTERPRETATION

Recurrence quantification analysis can be used to assess neuromuscular differences between limbs in patients who have undergone anterior cruciate ligament reconstruction. Our findings offer further evidence that there are changes to the neuromuscular system which persist following reconstruction. Further investigation is needed to establish thresholds of determinism and entropy values needed for safe return to sport and to evaluate the utility of recurrence quantification analysis as a return to sport criterion.

Nonlinear features in whistles produced by the short-beaked common dolphin (Delphinus delphis) off southeastern Brazil

Animal vocalizations have nonlinear characteristics responsible for features such as subharmonics, frequency jumps, biphonation, and deterministic chaos. This study describes the whistle repertoire of a short-beaked common dolphin (Delphinus delphis) group at Brazilian coast and quantifies the nonlinear features of these whistles. Dolphins were recorded for a total of 67 min around Cabo Frio, Brazil. We identify 10 basic categories of whistle, with 75 different types, classified according to their contour shape. Most (45) of these 75 types had not been reported previously for the species. The duration of the whistles ranged from 0.04 to 3.67 s, with frequencies of 3.05-29.75 kHz. Overall, the whistle repertoire presented here has one of the widest frequency ranges and greatest level of frequency modulation recorded in any study of D. delphis. All the nonlinear features sought during the study were confirmed, with at least one feature occurring in 38.4% of the whistles. The frequency jump was the most common feature (29.75% of the whistles) and the nonlinear time series analyses confirmed the deterministic chaos in the chaotic-like segments. These results indicate that nonlinearities are a relevant characteristic of these whistles, and that are important in acoustic communication.

On the forecastability of food insecurity

Food insecurity, defined as the lack of physical or economic access to safe, nutritious and sufficient food, remains one of the main challenges included in the 2030 Agenda for Sustainable Development. Near real-time data on the food insecurity situation collected by international organizations such as the World Food Programme can be crucial to monitor and forecast time trends of insufficient food consumption levels in countries at risk. Here, using food consumption observations in combination with secondary data on conflict, extreme weather events and economic shocks, we build a forecasting model based on gradient boosted regression trees to create predictions on the evolution of insufficient food consumption trends up to 30 days in to the future in 6 countries (Burkina Faso, Cameroon, Mali, Nigeria, Syria and Yemen). Results show that the number of available historical observations is a key element for the forecasting model performance. Among the 6 countries studied in this work, for those with the longest food insecurity time series, that is Syria and Yemen, the proposed forecasting model allows to forecast the prevalence of people with insufficient food consumption up to 30 days into the future with higher accuracy than a naive approach based on the last measured prevalence only. The framework developed in this work could provide decision makers with a tool to assess how the food insecurity situation will evolve in the near future in countries at risk. Results clearly point to the added value of continuous near real-time data collection at sub-national level.

Trunk stability in fatiguing frequency-dependent lifting activities

BACKGROUND

Work-related low-back disorders (WLBDs) are one of the most frequent and costly musculoskeletal conditions. It has been showed that WLBDs may occur when intervertebral or torso equilibrium is altered by a biomechanical perturbations or neuromuscular control error. The capacity to react to such disturbances is heavily determined by the spinal stability, provided by active and passive tissues and controlled by the central nervous system.

RESEARCH QUESTION

This study aims to investigate trunk stability through the Lyapunov's maximum exponent during repetitive liftings in relation to risk level, as well as to evaluate its ability to discriminate these risk levels.

METHODS

Fifteen healthy volunteers performed fatiguing lifting tasks at three different frequencies corresponding to low, medium, and high risk levels according to the National Institute for Occupational Safety and Health (NIOSH) equation. We investigated changes in spinal stability during fatiguing lifting tasks at different risk levels using the maximum Lyapunov's index (λ_Max) computed from trunk accelerations recorded by placing three IMUs at pelvis, lower and upper spine levels. A two-way repeated-measures ANOVA was performed to determine if there was any significant effect on λ_Max among the three risk levels and the time (start, mid, and end of the task). Additionally, we examined the Pearson's correlation of λ_Max with the trunk muscle co-activation, computed from trunk sEMG.

RESULTS

Our findings show an increase in trunk stability with increasing risk level and as the lifting task progressed over time. A negative correlation between λ_Max and trunk co-activation was observed which illustrates that the increase in spinal stability could be partially attributed to increased trunk muscle co-activation.

SIGNIFICANCE

This study highlights the possibility of generating stability measures from kinematic data as risk assessment features in fatiguing tasks which may prove useful to detect the risk of developing work-related low back pain disorders and allow the implementation of early ergonomic interventions.

A Brief Introductory Note on the Possible Chaotic Dynamics of the Muon Time Series of Cosmic Rays Measured at Sea Level by a Simple GMT Detector

After an investigation of the well-known basic properties of muons conducted by the standard model (SM), this paper presents the results obtained for the phase space reconstruction, for the correlation dimension and for the largest Lyapunov exponent of a muon time series detected for a period of about three years (2019–2021) in an Italian laboratory at the sea level. These results confirm that the dynamics of such a time series is chaotic in nature, and therefore open new perspectives in the study of cosmic rays. In the following studies, we will explore if such muon time series have a mono- or a multifractal regime with a complete analysis of all the parameters that usually involve such studies.

Deep learning delay coordinate dynamics for chaotic attractors from partial observable data

A common problem in time-series analysis is to predict dynamics with only scalar or partial observations of the underlying dynamical system. For data on a smooth compact manifold, Takens' theorem proves a time-delayed embedding of the partial state is diffeomorphic to the attractor, although for chaotic and highly nonlinear systems, learning these delay coordinate mappings is challenging. We utilize deep artificial neural networks (ANNs) to learn discrete time maps and continuous time flows of the partial state. Given training data for the full state, we also learn a reconstruction map. Thus, predictions of a time series can be made from the current state and several previous observations with embedding parameters determined from time-series analysis. The state space for time evolution is of comparable dimension to reduced order manifold models. These are advantages over recurrent neural network models, which require a high-dimensional internal state or additional memory terms and hyperparameters. We demonstrate the capacity of deep ANNs to predict chaotic behavior from a scalar observation on a manifold of dimension three via the Lorenz system. We also consider multivariate observations on the Kuramoto-Sivashinsky equation, where the observation dimension required for accurately reproducing dynamics increases with the manifold dimension via the spatial extent of the system.

Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology

Delay embedding methods are a staple tool in the field of time series analysis and prediction. However, the selection of embedding parameters can have a big impact on the resulting analysis. This has led to the creation of a large number of methods to optimize the selection of parameters such as embedding lag. This paper aims to provide a comprehensive overview of the fundamentals of embedding theory for readers who are new to the subject. We outline a collection of existing methods for selecting embedding lag in both uniform and non-uniform delay embedding cases. Highlighting the poor dynamical explainability of existing methods of selecting non-uniform lags, we provide an alternative method of selecting embedding lags that includes a mixture of both dynamical and topological arguments. The proposed method, Significant Times on Persistent Strands (SToPS), uses persistent homology to construct a characteristic time spectrum that quantifies the relative dynamical significance of each time lag. We test our method on periodic, chaotic, and fast-slow time series and find that our method performs similar to existing automated non-uniform embedding methods. Additionally, n-step predictors trained on embeddings constructed with SToPS were found to outperform other embedding methods when predicting fast-slow time series.

Has machine learning over-promised in healthcare? A critical analysis and a proposal for improved evaluation, with evidence from Parkinson’s disease

Adoption of artificial intelligence (AI) by the medical community has long been anticipated, endorsed by a stream of machine learning literature showcasing AI systems that yield extraordinary performance. However, many of these systems are likely over-promising and will under-deliver in practice. One key reason is the community's failure to acknowledge and address the presence of inflationary effects in the data. These simultaneously inflate evaluation performance and prevent a model from learning the underlying task, thus severely misrepresenting how that model would perform in the real world. This paper investigated the impact of these inflationary effects on healthcare tasks, as well as how these effects can be addressed. Specifically, we defined three inflationary effects that occur in medical data sets and allow models to easily reach small training losses and prevent skillful learning. We investigated two data sets of sustained vowel phonation from participants with and without Parkinson's disease, and revealed that published models which have achieved high classification performances on these were artificially enhanced due to the inflationary effects. Our experiments showed that removing each inflationary effect corresponded with a decrease in classification accuracy, and that removing all inflationary effects reduced the evaluated performance by up to 30%. Additionally, the performance on a more realistic test set increased, suggesting that the removal of these inflationary effects enabled the model to better learn the underlying task and generalize. Source code is available at https://github.com/Wenbo-G/pd-phonation-analysis under the MIT license.

Optimal sensor location and direction to accurately classify people with early-stage multiple sclerosis using gait stability

BACKGROUND

The local divergence exponent (LDE) has been used to assess gait stability in people with multiple sclerosis (pwMS). Although previous studies have consistently found that stability is lower in pwMS, inconsistent methodologies have been used to assess patients with a broad range of disability levels.

QUESTIONS

What sensor location and movement direction(s) are better able to classify pwMS at early stages of the disease?

METHODS

49 pwMS with EDSS ≤ 2.5 and 24 healthy controls walked overground for 5 min while 3D acceleration data was obtained from sensors placed at the sternum (STR) and lumbar (LUM) areas. Unidirectional (vertical [VT], mediolateral [ML], and anteroposterior [AP]) and 3-dimensional (3D) LDEs were calculated using STR and LUM data over 150 strides. ROC analyses were performed to assess classification models using single and combined LDEs, with and without velocity per lap (VEL_LAP) as a covariate.

RESULTS

Four models performed equally well by using combinations of VEL_LAP, LUM_3D, LUM_VT, LUM_ML, LUM_AP, STR_ML, and STR_AP (AUC = 0.879). The best model using single sensor LDEs included VEL_LAP, STR_3D, STR_ML, and STR_AP (AUC = 0.878), whereas using VEL_LAP + STR_VT (AUC = 0.869) or VEL_LAP + STR_3D (AUC=0.858) performed best using a single LDE.

SIGNIFICANCE

The LDE offers an alternative to currently insensitive tests of gait impairment in pwMS at early stages, when deterioration is not clinically evident. For clinical purposes, the implementation of this measure can be simplified using a single sensor at the sternum and a single LDE measure, but speed should be considered. Longitudinal studies to determine the predictive power and responsiveness of the LDE to MS progression are still needed.

Considerations for Applying Entropy Methods to Temporally Correlated Stochastic Datasets

The goal of this paper is to highlight considerations and provide recommendations for analytical issues that arise when applying entropy methods, specifically Sample Entropy (SampEn), to temporally correlated stochastic datasets, which are representative of a broad range of biomechanical and physiological variables. To simulate a variety of processes encountered in biomechanical applications, autoregressive fractionally integrated moving averaged (ARFIMA) models were used to produce temporally correlated data spanning the fractional Gaussian noise/fractional Brownian motion model. We then applied ARFIMA modeling and SampEn to the datasets to quantify the temporal correlations and regularity of the simulated datasets. We demonstrate the use of ARFIMA modeling for estimating temporal correlation properties and classifying stochastic datasets as stationary or nonstationary. We then leverage ARFIMA modeling to improve the effectiveness of data cleaning procedures and mitigate the influence of outliers on SampEn estimates. We also emphasize the limitations of SampEn to distinguish among stochastic datasets and suggest the use of complementary measures to better characterize the dynamics of biomechanical variables. Finally, we demonstrate that parameter normalization is not an effective procedure for increasing the interoperability of SampEn estimates, at least not for entirely stochastic datasets.

Recurrence Quantification Analysis of Center of Pressure Trajectories for Balance and Fall-Risk Assessment in Young and Older Adults

The prevalence and impact of balance impairments and falls in older adults have motivated several studies on the characterization of human balance. This study aimed to determine the ability of recurrence quantification analysis (RQA) measures to characterize balance control during quiet standing in young and older adults and to discriminate between different fall risk groups. We analyze center pressure trajectories in the medial-lateral and anterior-posterior directions from a publicly available static posturography dataset that contains tests acquired under four vision-surface testing conditions. Participants were retrospectively classified as young adults (age< 60, n=85), non-fallers (age≥60, falls=0, n=56), and fallers (age≥60, falls≥1, n=18). Mixed ANOVA and post hoc analyzes were performed to test for differences between groups. For CoP fluctuations in the anterior-posterior direction, all RQA measures showed significantly higher values for young than older adults when standing on a compliant surface, indicating less predictable and stable balance control among seniors under testing conditions where sensory information is restricted or altered. However, no significant differences between non-fallers and fallers were observed. These results support the use of RQA to characterize balance control in young and old adults, but not to discriminate between different fall risk groups.

Chaos and complexity in the dynamics of nonlinear Alfvén waves in a magnetoplasma

The nonlinear dynamics of circularly polarized dispersive Alfvén wave (AW) envelopes coupled to the driven ion-sound waves of plasma slow response is studied in a uniform magnetoplasma. By restricting the wave dynamics to a few number of harmonic modes, a low-dimensional dynamical model is proposed to describe the nonlinear wave-wave interactions. It is found that two subintervals of the wave number of modulation k of AW envelope exist, namely, (3/4)k_c<k<k_c and 0<k<(3/4)k_c, where k_c is the critical value of k below which the modulational instability (MI) occurs. In the former, where the MI growth rate is low, the periodic and/or quasi-periodic states are shown to occur, whereas the latter, where the MI growth is high, brings about the chaotic states. The existence of these states is established by the analyses of Lyapunov exponent spectra together with the bifurcation diagram and phase-space portraits of dynamical variables. Furthermore, the complexities of chaotic phase spaces in the nonlinear motion are measured by the estimations of the correlation dimension as well as the approximate entropy and compared with those for the known Hénon map and the Lorenz system in which a good qualitative agreement is noted. The chaotic motion, thus, predicted in a low-dimensional model can be a prerequisite for the onset of Alfvénic wave turbulence to be observed in a higher dimensional model that is relevant in the Earth's ionosphere and magnetosphere.

Cardiotocography analysis by empirical dynamic modeling and Gaussian processes

Introduction: During labor, fetal heart rate (FHR) and uterine activity (UA) can be continuously monitored using Cardiotocography (CTG). This is the most widely adopted approach for electronic fetal monitoring in hospitals. Both FHR and UA recordings are evaluated by obstetricians for assessing fetal well-being. Due to the complex and noisy nature of these recordings, the evaluation by obstetricians suffers from high interobserver and intraobserver variability. Machine learning is a field that has seen unprecedented advances in the past two decades and many efforts have been made in computerized analysis of CTG using machine learning methods. However, in the literature, the focus is often only on FHR signals unlike in evaluations performed by obstetricians where the UA signals are also taken into account. Methods: Machine learning is a field that has seen unprecedented advances in the past two decades and many efforts have been made in computerized analysis of CTG using machine learning methods. However, in the literature, the focus is often only on FHR signals unlike in evaluations performed by obstetricians where the UA signals are also taken into account. In this paper, we propose to model intrapartum CTG recordings from a dynamical system perspective using empirical dynamic modeling with Gaussian processes, which is a Bayesian nonparametric approach for estimation of functions. Results and Discussion: In the context of our paper, Gaussian processes are capable for simultaneous estimation of the dimensionality of attractor manifolds and reconstructing of attractor manifolds from time series data. This capacity of Gaussian processes allows for revealing causal relationships between the studied time series. Experimental results on real CTG recordings show that FHR and UA signals are causally related. More importantly, this causal relationship and estimated attractor manifolds can be exploited for several important applications in computerized analysis of CTG recordings including estimating missing FHR samples, recovering burst errors in FHR tracings and characterizing the interactions between FHR and UA signals.