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

Nonlinear dynamics in Divisia monetary aggregates: an application of recurrence quantification analysis

We construct recurrence plots (RPs) and conduct recurrence quantification analysis (RQA) to investigate the dynamic properties of the new Center for Financial Stability (CFS) Divisia monetary aggregates for the United States. In this study, we use the latest vintage of Divisia aggregates, maintained within CFS. We use monthly data, from January 1967 to December 2020, which is a sample period that includes the extreme economic events of the 2007-2009 global financial crisis. We then make comparisons between narrow and broad Divisia money measures and find evidence of a nonlinear but reserved possible chaotic explanation of their origin. The application of RPs to broad Divisia monetary aggregates encompasses an additional drift structure around the global financial crisis in 2008. Applying the moving window RQA to the growth rates of narrow and broad Divisia monetary aggregates, we identify periods of changes in data-generating processes and associate such changes to monetary policy regimes and financial innovations that occurred during those times.

Order and disorder in the evolution of online knowledge community: an investigation of the chaotic behavior in social tagging systems with evidence of stack overflow

Purpose

Online question-and-answer (Q&A) communities serve as important channels for knowledge diffusion. The purpose of this study is to investigate the dynamic development process of online knowledge systems and explore the final or progressive state of system development. By measuring the nonlinear characteristics of knowledge systems from the perspective of complexity science, the authors aim to enrich the perspective and method of the research on the dynamics of knowledge systems, and to deeply understand the behavior rules of knowledge systems.

Design/methodology/approach

The authors collected data from the programming-related Q&A site Stack Overflow for a ten-year period (2008–2017) and included 48,373 tags in the analyses. The number of tags is taken as the time series, the correlation dimension and the maximum Lyapunov index are used to examine the chaos of the system and the Volterra series multistep forecast method is used to predict the system state.

Findings

There are strange attractors in the system, the whole system is complex but bounded and its evolution is bound to approach a relatively stable range. Empirical analyses indicate that chaos exists in the process of knowledge sharing in this social labeling system, and the period of change over time is about one week.

Originality/value

This study contributes to revealing the evolutionary cycle of knowledge stock in online knowledge systems and further indicates how this dynamic evolution can help in the setting of platform mechanics and resource inputs.

Correlated SVD and Its Application in Bearing Fault Diagnosis

The singular value decomposition (SVD) based on the Hankel matrix is commonly used in signal processing and fault diagnosis. The noise reduction performance of SVD based on the Hankel matrix is affected by three factors: the reconstruction component(s), the structure of the Hankel matrix, and the point number of the analysis data. In this article, the three influencing factors are systematically studied, and a method based on correlated SVD (C-SVD) is proposed and successfully applied to bearing fault diagnosis. First, perform SVD analysis on the collected original signal. Then, the reconstructed component(s) determination method of SVD based on the combination of singular value ratio (SVR) and correlation coefficient is proposed. Then, based on the SVR, using the envelope kurtosis as the indicator, the optimal structure of the Hankel matrix (number of rows and columns) is studied. Then, the number of data points of the analysis signal is discussed, and the constraint range is given. Finally, the envelope power spectrum analysis is performed on the reconstructed signal to extract the fault features. The proposed C-SVD method is compared with the existing typical methods and applied to the simulated signal and the actual bearing fault signal, and its superiority is verified.

Parliamentary roll-call voting as a complex dynamical system: The case of Chile

A method is proposed to study the temporal variability of legislative roll-call votes in a parliament from the perspective of complex dynamical systems. We studied the Chilean Chamber of Deputies' by analyzing the agreement ratio and the voting outcome of each vote over the last 19 years with a Recurrence Quantification Analysis and an entropy analysis (Sample Entropy). Two significant changes in the temporal variability were found: one in 2014, where the voting outcome became more recurrent and with less entropy, and another in 2018, where the agreement ratio became less recurrent and with higher entropy. These changes may be directly related to major changes in the Chilean electoral system and the composition of the Chamber of Deputies, given that these changes occurred just after the first parliamentary elections with non-compulsory voting (2013 elections) and the first elections with a proportional system in conjunction with an increase in the number of deputies (2017 elections) were held.

Quantifying workload using nonlinear dynamical measures of biomechanical parameters during cycling on a roller trainer

The aim of the present study was to determine the effectiveness of nonlinear parameters in distinguishing individual workload in cycling by using bike-integrated sensor data. The investigation focused on two nonlinear parameters: The ML1, which analyzes the geometric median in phase space, and the maximum Lyapunov exponent as nonlinear measure of local system stability. We investigated two hypothesis: 1. ML1α, derived from kinematic crank data, is as good as ML1F, derived from force crank data, at distinguishing between individual load levels. 2. Increasing load during cycling leads to decreasing local system stability evidenced by linearly increasing maximal Lyapunov exponents generated from kinematic data. A maximal incremental cycling step test was conducted on an ergometer, generating complete datasets from 10 participants in a laboratory setting. Pedaling torque and kinematic data of the crank were recorded. ML1F, ML1α, and Lyapunov parameters (λst, λlt, ιst, ιlt) were calculated for each participant at comparable load levels. The results showed a significant linear increase in ML1α across three individual load levels, with a lower but still large effect compared to ML1F. The contrast analysis also confirmed a linearly increasing trend for λst across three load levels, but this was not confirmed for λlt. However, the intercepts ιst and ιlt of the short- and longterm divergence showed a statistically significant linear increase across the load levels. In summary, nonlinear parameters seem fundamentally suitable to distinguish individual load levels in cycling. It is concluded that higher load during cycling is associated with decreasing local system stability. These findings may aid in developing improved e-bike propulsion algorithms. Further research is needed to determine the impact of factors occurring in field application.

Reliability of Running Stability during Treadmill and Overground Running

Running stability is the ability to withstand naturally occurring minor perturbations during running. It is susceptible to external and internal running conditions such as footwear or fatigue. However, both its reliable measurability and the extent to which laboratory measurements reflect outdoor running remain unclear. This study aimed to evaluate the intra- and inter-day reliability of the running stability as well as the comparability of different laboratory and outdoor conditions. Competitive runners completed runs on a motorized treadmill in a research laboratory and overground both indoors and outdoors. Running stability was determined as the maximum short-term divergence exponent from the raw gyroscope signals of wearable sensors mounted to four different body locations (sternum, sacrum, tibia, and foot). Sacrum sensor measurements demonstrated the highest reliabilities (good to excellent; ICC = 0.85 to 0.91), while those of the tibia measurements showed the lowest (moderate to good; ICC = 0.55 to 0.89). Treadmill measurements depicted systematically lower values than both overground conditions for all sensor locations (relative bias = -9.8% to -2.9%). The two overground conditions, however, showed high agreement (relative bias = -0.3% to 0.5%; relative limits of agreement = 9.2% to 15.4%). Our results imply moderate to excellent reliability for both overground and treadmill running, which is the foundation of further research on running stability.

Forecasting for Chaotic Time Series Based on GRP-lstmGAN Model: Application to Temperature Series of Rotary Kiln

Rotary kiln temperature forecasting plays a significant part of the automatic control of the sintering process. However, accurate forecasts are difficult owing to the complex nonlinear characteristics of rotary kiln temperature time series. With the development of chaos theory, the prediction accuracy is improved by analyzing the essential characteristics of time series. However, the existing prediction methods of chaotic time series cannot fully consider the local and global characteristics of time series at the same time. Therefore, in this study, the global recurrence plot (GRP)-based generative adversarial network (GAN) and the long short-term memory (LSTM) combination method, named GRP-lstmGAN, are proposed, which can effectively display important information about time scales. First, the data is subjected to a series of pre-processing operations, including data smoothing. Then, transforming one-dimensional time series into two-dimensional images by GRP makes full use of the global and local information of time series. Finally, the combination of LSTM and improves GAN models for temperature time series prediction. The experimental results show that our model is better than comparison models.

Decoding the neural signatures of valence and arousal from portable EEG headset

Emotion classification using electroencephalography (EEG) data and machine learning techniques have been on the rise in the recent past. However, past studies use data from medical-grade EEG setups with long set-up times and environment constraints. This paper focuses on classifying emotions on the valence-arousal plane using various feature extraction, feature selection, and machine learning techniques. We evaluate different feature extraction and selection techniques and propose the optimal set of features and electrodes for emotion recognition. The images from the OASIS image dataset were used to elicit valence and arousal emotions, and the EEG data was recorded using the Emotiv Epoc X mobile EEG headset. The analysis is carried out on publicly available datasets: DEAP and DREAMER for benchmarking. We propose a novel feature ranking technique and incremental learning approach to analyze performance dependence on the number of participants. Leave-one-subject-out cross-validation was carried out to identify subject bias in emotion elicitation patterns. The importance of different electrode locations was calculated, which could be used for designing a headset for emotion recognition. The collected dataset and pipeline are also published. Our study achieved a root mean square score (RMSE) of 0.905 on DREAMER, 1.902 on DEAP, and 2.728 on our dataset for valence label and a score of 0.749 on DREAMER, 1.769 on DEAP, and 2.3 on our proposed dataset for arousal label.

Dynamical information flow within the magnetosphere-ionosphere system during magnetic storms

The direct role of successive intense magnetospheric substorms in injecting/energizing particles into the storm-time ring current is still debated and controversial. Whereas in the recent past it has been observed the absence of a net information flow between magnetic storms and substorms, previous in-situ satellite observations have evidenced that ionospheric-origin ions dominate the population of the ring current during the main phase of geomagnetic storms. As a matter of fact, the controversy arises mainly by the use of sophisticated data-driven techniques somewhat contradicting in-situ measurements. In this framework, the main aim of this work is to attempt an adaption of the powerful information-theoretic approach, i.e., the transfer entropy, in a consistent way with physics modeling and observations and to explore the possible motivations behind the underlying contradictions that emerge when these techniques are used. Our idea is to characterize the dynamics of the information flow within the magnetosphere-ionosphere system using a database of geomagnetic storms instead of considering a long time series of geomagnetic indices. We found a net information flow between the external driver and the geomagnetic indices and also between high and low latitude indices themselves, which turns out to be very well localized during the different phases of a magnetic storm.

Altered neuromuscular control in the vastus medialis following anterior cruciate ligament injury: A recurrence quantification analysis of electromyogram recruitment

BACKGROUND

Neuromuscular deficits exist following anterior cruciate ligament (ACL) injury. To observe these deficits, we examined nonlinear characteristics of vastus medialis electromyography (EMG) signals during submaximal isometric knee extensor contractions. Our purpose was to examine if determinism and entropy in EMG signals reflected neuromuscular control deficits in individuals with ACL-deficient limbs.

METHODS

24 participants (12 male, 12 female, mean age = 18.8 ± 3.1 years) with unilaterally injured ACLs and 25 age-similar healthy controls (11 male, 14 female, mean age = 18.8 ± 3.1 years) volunteered. Isometric knee extensions were tested at 10%, 25%, 35%, and 50% maximum voluntary contractions. Surface electrodes adhered over the vastus medialis captured EMG signals. EMG data were processed with recurrence quantification analyses. Specifically, determinism (an index of system predictability) and entropy (an index of system disorder) were calculated from recurrence plots.

FINDINGS

Determinism and entropy in EMG signals were lower in the injured than uninjured limb, and lower than that from healthy controls (P < .05).

INTERPRETATION

Vastus medialis EMG signals from the injured limb were less predictable and less complex than those from healthy limbs. The findings reflect impaired neuromuscular control in the injured limb's quadriceps and are consistent with a 'loss of complexity' hypothesis in physiologic signals emanating from pathologic states. Determinism and entropy in EMG signals may represent biomarkers of one's neuromuscular control system.

Searching for Chaotic Behavior in the Ion Current Waveforms of a Hall Effect Thruster

The dynamics of the ion flux expelled by a 0.5 kW-class Hall thruster supplied with krypton was examined in a wide range of discharge voltages. A homemade Faraday probe installed onto a rotary arm was used for reconstructing angular profiles of the plasma plume 0.5 m downstream of the thruster exit plane. The time dependence of the ion current was measured along the thruster axis. For investigating the signal dynamics, a Fourier approach as well as methods of nonlinear time series analysis like bifurcation diagrams and recurrence plot techniques were applied, which are of interest for chaotic behavior identification. Along with the well-known breathing mode (10—30 kHz), other characteristic groups of oscillations were also detected. The bifurcation diagram revealed a drastic transition between large and small amplitude oscillating regimes while varying the discharge voltage from 550 to 700 V. In parallel to this transition, recurrent plots display a qualitative change from a periodic (or quasi periodic) oscillating regime to much less predictable dynamics.

Homology groups of embedded fractional Brownian motion

A well-known class of nonstationary self-similar time series is the fractional Brownian motion (fBm) considered to model ubiquitous stochastic processes in nature. Due to noise and trends superimposed on data and even sample size and irregularity impacts, the well-known computational algorithm to compute the Hurst exponent (H) has encountered superior results. Motivated by this discrepancy, we examine the homology groups of high-dimensional point cloud data (PCD), a subset of the unit D-dimensional cube, constructed from synthetic fBm data as a pipeline to compute the H exponent. We compute topological measures for embedded PCD as a function of the associated Hurst exponent for different embedding dimensions, time delays, and amount of irregularity existing in the dataset in various scales. Our results show that for a regular synthetic fBm, the higher value of the embedding dimension leads to increasing the H dependency of topological measures based on zeroth and first homology groups. To achieve a reliable classification of fBm, we should consider the small value of time delay irrespective of the irregularity presented in the data. More interestingly, the value of the scale for which the PCD to be path connected and the postloopless regime scale are more robust concerning irregularity for distinguishing the fBm signal. Such robustness becomes less for the higher value of the embedding dimension. Finally, the associated Hurst exponents for our topological feature vector for the S&P500 were computed, and the results are consistent with the detrended fluctuation analysis method.

Color Recurrence Plots for Bearing Fault Diagnosis

This paper presents bearing fault diagnosis using the image classification of different fault patterns. Feature extraction for image classification is carried out using a novel approach of Color recurrence plots, which is presented for the first time. Color recurrence plots are created using non-linear embedding of the vibration signals into delay coordinate space with variable time lags. Deep learning-based image classification is then performed by building the database of the extracted features of the bearing vibration signals in the form of Color recurrence plots. A Series of computational experiments are performed to compare the accuracy of bearing fault classification using Color recurrence plots. The standard bearing vibration dataset of Case Western Reserve University is used for those purposes. The paper demonstrates the efficacy and the accuracy of a new and unique approach of scalar time series extraction into two-dimensional Color recurrence plots for bearing fault diagnosis.

Utilizing machine learning algorithms to predict subject genetic mutation class from in silico models of neuronal networks

Background

Epilepsy is the fourth-most common neurological disorder, affecting an estimated 50 million patients globally. Nearly 40% of patients have uncontrolled seizures yet incur 80% of the cost. Anti-epileptic drugs commonly result in resistance and reversion to uncontrolled drug-resistant epilepsy and are often associated with significant adverse effects. This has led to a trial-and-error system in which physicians spend months to years attempting to identify the optimal therapeutic approach.

Objective

To investigate the potential clinical utility from the context of optimal therapeutic prediction of characterizing cellular electrophysiology. It is well-established that genomic data alone can sometimes be predictive of effective therapeutic approach. Thus, to assess the predictive power of electrophysiological data, machine learning strategies are implemented to predict a subject’s genetically defined class in an in silico model using brief electrophysiological recordings obtained from simulated neuronal networks.

Methods

A dynamic network of isogenic neurons is modeled in silico for 1-s for 228 dynamically modeled patients falling into one of three categories: healthy, general sodium channel gain of function, or inhibitory sodium channel loss of function. Data from previous studies investigating the electrophysiological and cellular properties of neurons in vitro are used to define the parameters governing said models. Ninety-two electrophysiological features defining the nature and consistency of network connectivity, activity, waveform shape, and complexity are extracted for each patient network and t-tests are used for feature selection for the following machine learning algorithms: Neural Network, Support Vector Machine, Gaussian Naïve Bayes Classifier, Decision Tree, and Gradient Boosting Decision Tree. Finally, their performance in accurately predicting which genetic category the subjects fall under is assessed.

Results

Several machine learning algorithms excel in using electrophysiological data from isogenic neurons to accurately predict genetic class with a Gaussian Naïve Bayes Classifier predicting healthy, gain of function, and overall, with the best accuracy, area under the curve, and F1. The Gradient Boosting Decision Tree performs the best for loss of function models indicated by the same metrics.

Conclusions

It is possible for machine learning algorithms to use electrophysiological data to predict clinically valuable metrics such as optimal therapeutic approach, especially when combining several models.

Local networks from different parts of the human cerebral cortex generate and share the same population dynamic

A major goal of neuroscience is to reveal mechanisms supporting collaborative actions of neurons in local and larger-scale networks. However, no clear overall principle of operation has emerged despite decades-long experimental efforts. Here, we used an unbiased method to extract and identify the dynamics of local postsynaptic network states contained in the cortical field potential. Field potentials were recorded by depth electrodes targeting a wide selection of cortical regions during spontaneous activities, and sensory, motor, and cognitive experimental tasks. Despite different architectures and different activities, all local cortical networks generated the same type of dynamic confined to one region only of state space. Surprisingly, within this region, state trajectories expanded and contracted continuously during all brain activities and generated a single expansion followed by a contraction in a single trial. This behavior deviates from known attractors and attractor networks. The state-space contractions of particular subsets of brain regions cross-correlated during perceptive, motor, and cognitive tasks. Our results imply that the cortex does not need to change its dynamic to shift between different activities, making task-switching inherent in the dynamic of collective cortical operations. Our results provide a mathematically described general explanation of local and larger scale cortical dynamic.

Complexity analysis of heartbeat-related signals in brain MRI time series as a potential biomarker for ageing and cognitive performance

Getting older affects both the structure of the brain and some cognitive capabilities. Until now, magnetic resonance imaging (MRI) approaches have been unable to give a coherent reflection of the cognitive declines. It shows the limitation of the contrast mechanisms used in most MRI investigations, which are indirect measures of brain activities depending on multiple physiological and cognitive variables. However, MRI signals may contain information of brain activity beyond these commonly used signals caused by the neurovascular response. Here, we apply a zero-spin echo (ZSE) weighted MRI sequence, which can detect heartbeat-evoked signals (HES). Remarkably, these MRI signals have properties only known from electrophysiology. We investigated the complexity of the HES arising from this sequence in two age groups; young (18-29 years) and old (over 65 years). While comparing young and old participants, we show that the complexity of the HES decreases with age, where the stability and chaoticity of these HES are particularly sensitive to age. However, we also found individual differences which were independent of age. Complexity measures were related to scores from different cognitive batteries and showed that higher complexity may be related to better cognitive performance. These findings underpin the affinity of the HES to electrophysiological signals. The profound sensitivity of these changes in complexity shows the potential of HES for understanding brain dynamics that need to be tested in more extensive and diverse populations with clinical relevance for all neurovascular diseases.

Supplementary Information

The online version contains supplementary material available at 10.1140/epjs/s11734-022-00696-2.

Non-Destructive Detection of Real Defects in Polymer Composites by Ultrasonic Testing and Recurrence Analysis

This paper presents results of ultrasonic non-destructive testing of carbon fibre-reinforced plastics (CFRPs) and glass-fibre reinforced plastics (GFRPs). First, ultrasonic C-scan analysis was used to detect real defects inside the composite materials. Next, the composite materials were subjected to drilling in the area of defect formation, and measured forces were used to analyse the drilling process using recurrence methods. Results have confirmed that recurrence methods can be used to detect defects formed inside a composite material during machining.

Complexity of locomotion activities in an outside-of-the-lab wearable motion capture dataset

Gait complexity is widely used to understand risk factors for injury, rehabilitation, the performance of assistive devices, and other matters of clinical interest. We analyze the complexity of out-of-the-lab locomotion activities via measures that have previously been used in gait analysis literature, as well as measures from other domains of data analysis. We categorize these broadly as quantifying either the intrinsic dimensionality, the variability, or the regularity, periodicity, or self-similarity of the data from a nonlinear dynamical systems perspective. We perform this analysis on a novel full-body motion capture dataset collected in out-of-the-lab conditions for a variety of indoor environments. This is a unique dataset with a large amount (over 24 h total) of data from participants behaving without low-level instructions in out-of-the-lab indoor environments. We show that reasonable complexity measures can yield surprising, and even profoundly contradictory, results. We suggest that future complexity analysis can use these guidelines to be more specific and intentional about what aspect of complexity a quantitative measure expresses. This will become more important as wearable motion capture technology increasingly allows for comparison of ecologically relevant behavior with lab-based measurements.

Chaos analysis of the brain topology in first-episode psychosis and clinical high risk patients

Structural MRI studies in first-episode psychosis (FEP) and in clinical high risk (CHR) patients have consistently shown volumetric abnormalities in frontal, temporal, and cingulate cortex areas. The aim of the present study was to employ chaos analysis for the identification of brain topology differences in people with psychosis. Structural MRI were acquired from 77 FEP, 73 CHR and 44 healthy controls (HC). Chaos analysis of the gray matter distribution was performed: First, the distances of each voxel from the center of mass in the gray matter image was calculated. Next, the distances multiplied by the voxel intensity were represented as a spatial-series, which then was analyzed by extracting the Largest-Lyapunov-Exponent (lambda). The lambda brain map depicts thus how the gray matter topology changes. Between-group differences were identified by (a) comparing the lambda brain maps, which resulted in statistically significant differences in FEP and CHR compared to HC; and (b) matching the lambda series with the Morlet wavelet, which resulted in statistically significant differences in the scalograms of FEP against CHR and HC. The proposed framework using spatial-series extraction enhances the between-group differences of FEP, CHR and HC subjects, verifies diagnosis-relevant features and may potentially contribute to the identification of structural biomarkers for psychosis.

Identifying causality drivers and deriving governing equations of nonlinear complex systems

Identifying and describing the dynamics of complex systems is a central challenge in various areas of science, such as physics, finance, or climatology. While machine learning algorithms are increasingly overtaking traditional approaches, their inner workings and, thus, the drivers of causality remain elusive. In this paper, we analyze the causal structure of chaotic systems using Fourier transform surrogates and three different inference techniques: While we confirm that Granger causality is exclusively able to detect linear causality, transfer entropy and convergent cross-mapping indicate that causality is determined to a significant extent by nonlinear properties. For the Lorenz and Halvorsen systems, we find that their contribution is independent of the strength of the nonlinear coupling. Furthermore, we show that a simple rationale and calibration algorithm are sufficient to extract the governing equations directly from the causal structure of the data. Finally, we illustrate the applicability of the framework to real-world dynamical systems using financial data before and after the COVID-19 outbreak. It turns out that the pandemic triggered a fundamental rupture in the world economy, which is reflected in the causal structure and the resulting equations.

Evaluation of Geometric Attractor Structure and Recurrence Analysis in Professional Dancers

BACKGROUND

Human motor systems contain nonlinear features. The purpose of this study was to evaluate the geometric structure of attractors and analyze recurrence in two different pirouettes (jazz and classic) performed by 15 professional dancers.

METHODS

The kinematics of the body's center of mass (CoM) and knee of the supporting leg (LKNE) during the pirouette were measured using the Vicon system. A time series of selected points were resampled, normalized, and randomly reordered. Then, every second time series was flipped to be combined with other time series and make a long time series out of the repetitions of a single task. The attractors were reconstructed, and the convex hull volumes (CHV) were counted for the CoM and LKNE for each pirouette in each direction. Recurrence quantification analysis (RQA) was used to extract additional information.

RESULTS

The CHVs calculated for the LKNE were significantly lower for the jazz pirouette. All RQA measures had the highest values for LKNE along the mediolateral axis for the jazz pirouette. This result underscores the high determinism, high motion recurrence, and complexity of this maneuver.

CONCLUSIONS

The findings offer new insight into the evaluation of the approximation of homogeneity in motion control. A high determinism indicates a highly stable and predictive motion trajectory.

A New Method for Determining the Embedding Dimension of Financial Time Series Based on Manhattan Distance and Recurrence Quantification Analysis

Identification of embedding dimension is helpful to the reconstruction of phase space. However, it is difficult to calculate the proper embedding dimension for the financial time series of dynamics. By this Letter, we suggest a new method based on Manhattan distance and recurrence quantification analysis for determining the embedding dimension. By the advantages of the above two tools, the new method can calculate the proper embedding dimension with the feature of stability, accuracy and rigor. Besides, it also has a good performance on the chaotic time series which has a high-dimensional attractors.

Reconstructing data-driven governing equations for cell phenotypic transitions: integration of data science and systems biology

Cells with the same genome can exist in different phenotypes and can change between distinct phenotypes when subject to specific stimuli and microenvironments. Some examples include cell differentiation during development, reprogramming for induced pluripotent stem cells and transdifferentiation, cancer metastasis and fibrosis progression. The regulation and dynamics of cell phenotypic conversion is a fundamental problem in biology, and has a long history of being studied within the formalism of dynamical systems. A main challenge for mechanism-driven modeling studies is acquiring sufficient amount of quantitative information for constraining model parameters. Advances in quantitative experimental approaches, especially high throughput single-cell techniques, have accelerated the emergence of a new direction for reconstructing the governing dynamical equations of a cellular system from quantitative single-cell data, beyond the dominant statistical approaches. Here I review a selected number of recent studies using live- and fixed-cell data and provide my perspective on future development.

Experimental Verification of the Impact of Radial Internal Clearance on a Bearing's Dynamics

This paper focuses on the influence of radial internal clearance on the dynamics of a rolling-element bearing. In the beginning, the 2-Degree of Freedom (DOF) model was studied, in which the clearance was treated as a bifurcation parameter. The derived nonlinear mathematical model is based on Hertzian contact theory and takes into consideration shape errors of rolling surfaces and eccentricity reflecting real operating conditions. The analysis showed characteristic dynamical behavior by specific clearance range, which reflects others in a low or high amplitude and can refer to the optimal clearance. The experimental validation was conducted with the use of a double row self-aligning ball bearing (SABB) NTN 2309SK in which the acceleration response was measured by various rotational velocities. The time series obtained from the mathematical model and the experiment were analyzed with the recurrence quantification analysis.

Research on Recurrence Plot Feature Quantization Method Based on Image Texture Analysis

The nonlinear time-series analysis method, based on the recurrence plot theory, has received great attention from researchers and has been successfully used in multiple fields. However, traditional recurrence plots that use Heaviside step functions to determine the recursive behavior of a point in the phase space have two problems: (1) Heaviside step functions produce a rigid boundary, resulting in information loss; and (2) the selection of the critical distance, ε, is crucial; if the selection is inappropriate, it will result in a low-dimensional dynamics error, and as of now, there exists no unified method for selecting this parameter. With regard to the problems described above, the novelty of this article lies in the following: (1) when determining the state-phase point recursiveness, a Gaussian function is used to replace the Heaviside function, thereby solving the rigidity and binary value problems of the recursive analysis results caused by the Heaviside step function; and (2) texture analysis is performed on a recurrence plot, new ways of studying complex system dynamics features are proposed, and a system of complex system dynamic-like measurement methods is built.

Local dynamic stability of the trunk after prolonged seating with axial load

Fatigue from prolonged seating with an axial load on the trunk may impair neuromuscular control and spine stability which may elevate risk of low back pain (LBP) for dynamic tasks following seating. The objective of this study was to assess local dynamic trunk stability using the maximum Lyapunov exponent (λ_MAX) with corresponding coactivation patterns to understand possible effects from prolonged seating. An increase in λ_MAX would indicate decreased stability. Twenty participants (10 male, 10 female) performed a controlled, cyclic sagittal flexion task at 40 cycles per minute before and after three hours of seating in a simulated helicopter-seating environment with a weighted vest. A statistically significant decrease was seen in λ_MAX (bits/s) (Pre-Test = 0.654 ± 0.172; Post-Test = 0.829 ± 0.268, p = 0.002), trunk cumulative coactivation index (unitless/s) (Pre-Test = 1.71 ± 0.97; Post-Test = 1.59 ± 0.96, p = 0.0095), and abdominal activation (normalized) (Pre-Test = 0.46 ± 0.17, Post-Test = 0.41 ± 0.18, p = 0.0146) post-seating exposure. Trunk extension was reduced (∼4°, p = 0.0004) during the post-seating cyclic test with slight corresponding increases in flexion. This study provides evidence of potential effects of fatigue from prolonged seating to neuromuscular control, which may have implications for occupations requiring highly dynamic tasks after prolonged seated postures. Future studies would repeat the tests with dynamic environments (i.e., vibration), test the cyclic flexion protocols with different seating interventions, and continue to test the approach to develop a tool to assess back impairment or intervention effectiveness.

Hourly solar irradiation forecast using hybrid local gravitational clustering and group method of data handling methods

The foundation for many solar energy uses as well as economic and environmental concerns is global solar irradiation information. However, due to solar irradiation and measurement variations, reliable worldwide statistics on solar irradiation are frequently impossible or challenging to acquire. In addition, more precise forecasts of solar irradiation play an increasingly important role in electric energy planning and management due to integrating photovoltaic solar systems into power networks. Hence, this paper proposes a new hybrid model for 1-h ahead solar irradiation forecasting called LGC-GMDH (local gravitational clustering-group method of data handling). The novel LGC-GMDH model is based on local clustering that adequately captures the underlying features of the solar irradiation time series. Each cluster is then forecasted using the GMDH method, which is a self-organized system capable of handling very complicated nonlinear problems. Finally, these local forecasts are reconstructed in order to obtain the global forecast. Comparative study between the proposed model and the traditional individual models such as backpropagation neural network (BP), supporting vector machines (SVM), long short-term memory (LTSM), and hybrid models such as BP-MLP, RNN-MLP, LSTM-MLP hybrid wavelet packet decomposition (WPD), convolutional neural network (CNN) with LSTM-MLP, and ANFIS clustering shows that the proposed model overcomes conventional model deficiencies and achieves more precise predicting outcome.

Cardio-Hypothalamic-Pituitary Coupling during Rest and in Response to Exercise

The objective of this study was to examine cardio hypothalamic-pituitary coupling and to better understand how the temporal relations between these systems are altered during rest and exercise conditions. An intensive within subjects study design was used. Seven adult males completed two visits, each consisting of either a 24 h period of complete rest or a 24 h period containing a high-intensity exercise bout. An intravenous catheter was used to collect serum samples every 10 min throughout the 24 h period (i.e., 145 samples/person/condition) to assess growth hormone (GH) dynamics throughout the 24 h period. Cardiac dynamics were also collected throughout the 24 h period and epoched into 3 min windows every 10 min, providing serial short-time measurements of heart rate variability (HRV) concurrent to the GH sampling. The standard deviation of the normal RR interval (SDNN), the root mean square of successive differences (rMSSD), and sample entropy (SampEn) was calculated for each epoch and used to create new profiles. The dynamics of these profiles were individually quantified using SampEn and recurrence quantification analysis (RQA). To address our central question, the coupling between these profiles with GH was assessed using cross-SampEn and cross-RQA (cRQA). A comparison between the epoched HRV profiles indicated a main effect between profiles for sample entropy (p < 0.001) and several measures from RQA. An interaction between profile and condition was observed for cross-SampEn (p = 0.04) and several measures from cRQA. These findings highlight the potential application of epoched HRV to assess changes in cardiac dynamics, with specific applications to assessing cardio hypothalamic-pituitary coupling.

Deep multi-modal learning for joint linear representation of nonlinear dynamical systems

Dynamical systems pervasively seen in most real-life applications are complex and behave by following certain evolution rules or dynamical patterns, which are linear, non-linear, or stochastic. The underlying dynamics (or evolution rule) of such complex systems, if found, can be used for understanding the system behavior, and furthermore for system prediction and control. It is common to analyze the system's dynamics through observations in different modality approaches. For instance, to recognize patient deterioration in acute care, it usually relies on monitoring and analyzing vital signs and other observations, such as blood pressure, heart rate, respiration, and electroencephalography. These observations convey the information describing the same target system, but the dynamics is not able to be directly characterized due to high complexity of individual modality and maybe time-delay interactions among modalities. In this work, we suppose that the state behavior of a dynamical system follows an intrinsic dynamics shared among these modalities. We specifically propose a new deep auto-encoder framework using the Koopman operator theory to derive the joint linear dynamics for a target system in a space spanned by the intrinsic coordinates. The proposed method aims to reconstruct the original system states by learning the information provided among multiple modalities. Furthermore, with the derived intrinsic dynamics, our method is capable of restoring the missing observations within and across modalities, and used for predicting the future states of the system that follows the same evolution rule.

Experimental Diagnosis on Combustion Characteristic of Shock Wave Focusing Initiation Engine

A shock wave focusing initiation engine was assembled and tested in an experimental program. The effective pyrolysis rate of the pre-combustor was evaluated over a range of supplementary fuel ratio in this paper. Results highlight two operational modes of the resonant cavity: (1) pulsating combustion mode, (2) stable combustion mode. The appearance of the two combustion modes is jointly affected by the flow and the structural characteristic value of the combustion chamber. This paper uses images, time-frequency analysis, and nonlinear time series analysis methods to identify and distinguish these two combustion modes. It is believed that the interaction between the combustion chamber and the supply plenum is the probable reason for different combustion modes. The experiment has found that structural parameters and import flow parameters have an impact on the initiation of the combustion chamber. Increasing the injection pressure can appropriately broaden the fuel-rich boundary of initiation. Low equivalence ratio and high injection pressure can also appropriately increase the combustion working frequency in a small range. From the perspective of pressure utilization, under the premise of ensuring successful initiation, injection pressure should not be too high.

Photoplethysmogram Recording Length: Defining Minimal Length Requirement from Dynamical Characteristics

Photoplethysmography is a widely used technique to noninvasively assess heart rate, blood pressure, and oxygen saturation. This technique has considerable potential for further applications—for example, in the field of physiological and mental health monitoring. However, advanced applications of photoplethysmography have been hampered by the lack of accurate and reliable methods to analyze the characteristics of the complex nonlinear dynamics of photoplethysmograms. Methods of nonlinear time series analysis may be used to estimate the dynamical characteristics of the photoplethysmogram, but they are highly influenced by the length of the time series, which is often limited in practical photoplethysmography applications. The aim of this study was to evaluate the error in the estimation of the dynamical characteristics of the photoplethysmogram associated with the limited length of the time series. The dynamical properties were evaluated using recurrence quantification analysis, and the estimation error was computed as a function of the length of the time series. Results demonstrated that properties such as determinism and entropy can be estimated with an error lower than 1% even for short photoplethysmogram recordings. Additionally, the lower limit for the time series length to estimate the average prediction time was computed.

Nitrogen-enriched discharges from a highly managed watershed intensify red tide (Karenia brevis) blooms in southwest Florida

Karenia brevis blooms on Florida's Gulf Coast severely affect regional ecosystems, coastal economies, and public health, and formulating effective management and policy strategies to address these blooms requires an advanced understanding of the processes driving them. Recent research suggests that natural processes explain offshore bloom initiation and shoreward transport, while anthropogenic nutrient inputs may intensify blooms upon arrival along the coast. However, past correlation studies have failed to detect compelling evidence linking coastal blooms to watershed covariates indicative of anthropogenic inputs. We explain why correlation is neither necessary nor sufficient to demonstrate a causal relationship-i.e., a persistent pattern of interaction governed by deterministic rules-and pursue an empirical investigation leveraging the fact that systematic temporal patterns may reveal systematic cause-and-effect relationships. Using time series derived from in-situ sample data, we applied singular spectrum analysis-a non-parametric spectral decomposition method-to recover deterministic signals in the dynamics of K. brevis blooms and upstream water quality and discharge covariates in the Charlotte Harbor region between 2012 and 2021. Next, we applied causal analysis methods based on chaos theory-i.e., convergent cross-mapping and S-mapping-to detect and quantify persistent, state-dependent interaction regimes between coastal blooms and watershed covariates. We discovered that nitrogen-enriched Caloosahatchee River discharges have consistently intensified K. brevis blooms to varying degrees over time. River discharge was typically most influential at the earliest stages of blooms, while total nitrogen concentrations exerted the strongest influence during blooms' growth/maintenance stages. These results indicate that discharges and nitrogen inputs influence blooms through distinct yet synergistic causal mechanisms. Additionally, we traced this anthropogenic influence upstream to Lake Okeechobee (which discharges to the Caloosahatchee River) and the Kissimmee River basin (which drains into Lake Okeechobee), suggesting that watershed-scale nutrient management and modifications to Lake Okeechobee discharge protocols will likely be necessary to mitigate coastal blooms.

NoLiTiA: An Open-Source Toolbox for Non-linear Time Series Analysis

In many scientific fields including neuroscience, climatology or physics, complex relationships can be described most parsimoniously by non-linear mechanics. Despite their relevance, many neuroscientists still apply linear estimates in order to evaluate complex interactions. This is partially due to the lack of a comprehensive compilation of non-linear methods. Available packages mostly specialize in only one aspect of non-linear time-series analysis and most often require some coding proficiency to use. Here, we introduce NoLiTiA, a free open-source MATLAB toolbox for non-linear time series analysis. In comparison to other currently available non-linear packages, NoLiTiA offers (1) an implementation of a broad range of classic and recently developed methods, (2) an implementation of newly proposed spatially and time-resolved recurrence amplitude analysis and (3) an intuitive environment accessible even to users with little coding experience due to a graphical user interface and batch-editor. The core methodology derives from three distinct fields of complex systems theory, including dynamical systems theory, recurrence quantification analysis and information theory. Besides established methodology including estimation of dynamic invariants like Lyapunov exponents and entropy-based measures, such as active information storage, we include recent developments of quantifying time-resolved aperiodic oscillations. In general, the toolbox will make non-linear methods accessible to the broad neuroscientific community engaged in time series processing.

Passive Exoskeleton-Assisted Gait Shows a Unique Interlimb Coordination Signature Without Restricting Regular Walking

Exoskeleton assistive devices have been developed as a potential approach to solve gait deficits like paretic propulsion and reduced speed. However, it is unclear how these devices affect inter-limb coordination. The duration and the synchrony of gait coordination was assessed during passive exoskeleton-assisted walking in healthy young individuals. It was hypothesized that inter-limb coordination would be reduced in comparison to normal walking without assistance, thus demonstrating gait with exoskeleton to be more explorative and flexible. Eighteen participants were divided into two groups (EXO: n = 9; NO EXO: n = 9) and performed a 5-min walking trial at a preferred walking speed after a familiarization trial. The duration of inter-limb coordination was examined using cross-recurrence quantification analysis and the synchrony was measured using cross sample entropy. There were no significant differences in spatiotemporal measurements between the two groups. However, in comparison to the no exoskeleton group, there was a reduction in the duration of coordination (mean diagonal length: p < 0.01) and the synchrony of coordination (entropy value: p < 0.05) in the exoskeleton group. These results indicate that exoskeletal-assisted gait is characterized by reduced inter-limb coordination possibly for allowing gait patterns to be more explorative and flexible. This is important in rehabilitation of patients who suffer from coordination deficits.

Effects of barefoot vs. shod walking during indoor and outdoor conditions in younger and older adults

BACKGROUND

Gait stability and variability measures in barefoot and shod locomotion are frequently investigated in younger but rarely in older adults. Moreover, most studies examine gait measures in laboratory settings instead of real-life settings.

RESEARCH QUESTIONS

How are gait stability and variability parameters affected by footwear compared to barefoot walking in younger and older adults as well as under indoor vs. outdoor conditions?

METHODS

Healthy younger (<35 years) and older adults (>65 years) participated in the randomised within-subject study design. Participants conducted consecutive 25 m walking trials barefoot and with standardised footwear inside and outside. Inertial measurement units were mounted on the participant's foot and used to calculate local dynamic stability (LDS), velocity and minimal toe clearance (MTC), stride length and stride time, including variabilities for these parameters. Linear mixed models were calculated.

RESULTS

Data of 32 younger (17 female, 15 male, age: 30 ± 4 years) and 42 older participants (24 female, 18 male, age: 71 ± 4 years) were analysed. MTC variability was higher in shod conditions compared to barefoot (p = 0.048) and in outdoor conditions (p < 0.001). LDS was different between age groups (p < 0.001). Gait velocity and MTC were higher in shod and outdoor conditions (both p < 0.001). Stride length and time were higher in shod conditions (both p < 0.001) and different between outdoor vs. indoor (longer stride length and shorter stride time outdoor, both (p < 0.001) as well as age groups (shorter stride length (p < 0.021) and stride time in older adults (p < 0.001).

SIGNIFICANCE

Results suggest that gait stability and variability in older and younger adults are acutely affected by footwear vs. barefoot and indoor vs. outdoor walking conditions, indicating a high adaptiveness of these parameters to different experimental conditions. Consequently, future studies should be careful with generalising results obtained under certain conditions. Findings stress the clinical potential of barefoot walking.

Improving time series prediction accuracy for the maxima of a flow by reconstructions using local cross sections

Despite a long history of time series analysis/prediction, theoretically few is known on how to predict the maxima better. To predict the maxima of a flow more accurately, we propose to use its local cross sections or plates the flow passes through. First, we provide a theoretical underpinning for the observability using local cross sections. Second, we show that we can improve short-term prediction of local maxima by employing a generalized prediction error, which weighs more for the larger values. The proposed approach is demonstrated by rainfalls, where heavier rains may cause casualties.

Model selection of chaotic systems from data with hidden variables using sparse data assimilation

Many natural systems exhibit chaotic behavior, including the weather, hydrology, neuroscience, and population dynamics. Although many chaotic systems can be described by relatively simple dynamical equations, characterizing these systems can be challenging due to sensitivity to initial conditions and difficulties in differentiating chaotic behavior from noise. Ideally, one wishes to find a parsimonious set of equations that describe a dynamical system. However, model selection is more challenging when only a subset of the variables are experimentally accessible. Manifold learning methods using time-delay embeddings can successfully reconstruct the underlying structure of the system from data with hidden variables, but not the equations. Recent work in sparse-optimization based model selection has enabled model discovery given a library of possible terms, but regression-based methods require measurements of all state variables. We present a method combining variational annealing-a technique previously used for parameter estimation in chaotic systems with hidden variables-with sparse-optimization methods to perform model identification for chaotic systems with unmeasured variables. We applied the method to ground-truth time-series simulated from the classic Lorenz system and experimental data from an electrical circuit with Lorenz-system like behavior. In both cases, we successfully recover the expected equations with two measured and one hidden variable. Application to simulated data from the Colpitts oscillator demonstrates successful model selection of terms within nonlinear functions. We discuss the robustness of our method to varying noise.

Deep-learning-based seizure detection and prediction from electroencephalography signals

Electroencephalography (EEG) is among the main tools used for analyzing and diagnosing epilepsy. The manual analysis of EEG must be conducted by highly trained clinicians or neuro-physiologists; a process that is considered to have a comparatively low inter-rater agreement. Furthermore, the new data interpretation consumes an excessive amount of time and resources. Hence, an automatic seizure detection and prediction system can improve the quality of patient care in terms of shortening the diagnosis period, reducing manual errors, and automatically detecting debilitating events. Moreover, for patient treatment, it is important to alert the patients of epilepsy seizures prior to seizure occurrence. Various distinguished studies presented good solutions for two-class seizure detection problems with binary classification scenarios. To deal with these challenges, this paper puts forward effective approaches for EEG signal classification for normal, pre-ictal, and ictal activities. Three models are presented for the classification task. Two of them are patient-specific, while the third one is patient non-specific, which makes it better for the general classification tasks. The two-class classification is implemented between normal and pre-ictal activities for seizure prediction and between normal and ictal activities for seizure detection. A more generalized three-class classification framework is considered to identify all EEG signal activities. The first model depends on a Convolutional Neural Network (CNN) with residual blocks. It contains thirteen layers with four residual learning blocks. It works on spectrograms of EEG signal segments. The second model depends on a CNN with three layers. It also works on spectrograms. On the other hand, the third model depends on Phase Space Reconstruction (PSR) to eliminate the limitations of the spectrograms used in the first models. A five-layer CNN is used with this strategy. The advantage of the PSR is the direct projection from the time domain, which keeps the main trend of different signal activities. The third model deals with all signal activities, and it was tested for all patients of the CHB-MIT dataset. It has a superior performance compared to the first models and the state-of-the-art models.

Dam deformation forecasting using SVM-DEGWO algorithm based on phase space reconstruction

A hybrid model integrating chaos theory, support vector machine (SVM) and the difference evolution grey wolf optimization (DEGWO) algorithm is developed to analyze and predict dam deformation. Firstly, the chaotic characteristics of the dam deformation time series will be identified, mainly using the Lyapunov exponent method, the correlation dimension method and the kolmogorov entropy method. Secondly, the hybrid model is established for dam deformation forecasting. Taking SVM as the core, the deformation time series is reconstructed in phase space to determine the input variables of SVM, and the GWO algorithm is improved to realize the optimization of SVM parameters. Prior to this, the effectiveness of DEGWO algorithm based on the fusion of the difference evolution (DE) and GWO algorithm has been verified by 15 sets of test functions in CEC 2005. Finally, take the actual monitoring displacement of Jinping I super-high arch dam as examples. The engineering application examples show that the PSR-SVM-DEGWO model established performs better in terms of fitting and prediction accuracy compared with existing models.

Chaotic dynamics of small-sized charged Yukawa dust clusters

In a recent work [Maity et al., Phys. Rev. E 102(2), 023213 (2020)] the equilibrium of a cluster of charged dust particles mutually interacting with screened Coulomb force and radially confined by an externally applied electric field in a two-dimensional configuration was studied. It was shown that the particles arranged themselves on discrete radial rings forming a lattice structure. In some cases with a specific number of particles, no static equilibrium was observed. Instead, angular rotation of particles positioned at various rings was observed. In a two-ringed structure, it was shown that the direction of rotation of the particles positioned in different rings was opposite. The direction of rotation was also observed to change apparently at random time intervals. A detailed characterization of the dynamics of small-sized Yukawa clusters, with a varying number of particles and different strengths of the confining force, has been carried out. The correlation dimension and the largest Lyapunov index for the dynamical state have been evaluated to demonstrate that the dynamics is chaotic. This is interesting considering that the charged microparticles have many applications in a variety of industrial processes.

How deterministic is the Earth ionosphere's response to solar activity?

This contribution is aimed at an analysis of the dynamics of free-electron density fluctuations in the ionospheric critical plasma frequency f0F2 by using some tools from the theory of nonlinear dynamical systems. The results suggest the existence of low-dimensional attractors that point to a characterization of the free electron density fluctuations in the f0F2 as a deterministic chaotic system. The study carried out focused on the response of the ionosphere to solar activity as a function of the ascending and descending phases of the solar cycle.

Replication in Energy Markets: Use and Misuse of Chaos Tools

As pointed out by many researchers, replication plays a key role in the credibility of applied sciences and the confidence in all research findings. With regard, in particular, to energy finance and economics, replication papers are rare, probably because they are hampered by inaccessible data, but their aim is crucial. We consider two ways to avoid misleading results on the ostensible chaoticity of price series. The first one is represented by the proper mathematical definition of chaos and the related theoretical background, while the latter is represented by the hybrid approach that we propose here-i.e., consisting of considering the dynamical system underlying the price time series as a deterministic system with noise. We find that both chaotic and stochastic features coexist in the energy commodity markets, although the misuse of some tests in the established practice in the literature may say otherwise.

Continuity Scaling: A Rigorous Framework for Detecting and Quantifying Causality Accurately

Data-based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to science, engineering, and beyond. Inspired by the widely used methodology in recent years, the cross-map-based techniques, we develop a general framework to advance towards a comprehensive understanding of dynamical causal mechanisms, which is consistent with the natural interpretation of causality. In particular, instead of measuring the smoothness of the cross-map as conventionally implemented, we define causation through measuring the scaling law for the continuity of the investigated dynamical system directly. The uncovered scaling law enables accurate, reliable, and efficient detection of causation and assessment of its strength in general complex dynamical systems, outperforming those existing representative methods. The continuity scaling-based framework is rigorously established and demonstrated using datasets from model complex systems and the real world.

The effects of mobile phone use on motor variability patterns during gait

Mobile phone use affects the dynamics of gait by impairing visual control of the surrounding environment and introducing additional cognitive demands. Although it has been shown that using a mobile phone alters whole-body dynamic stability, no clear information exists on its impacts on motor variability during gait. This study aimed at assessing the impacts of various types of mobile phone use on motor variability during gait; quantified using the short- and long-term Lyapunov Exponent (λ_S and λ_L) of lower limb joint angles and muscle activation patterns, as well as the centre of mass position. Fourteen females and Fifteen males (27.72 ± 4.61 years, body mass: 70.24 ± 14.13 Kg, height: 173.31 ± 10.97 cm) walked on a treadmill under six conditions: normal walking, normal walking in low-light, walking while looking at the phone, walking while looking at the phone in low-light, walking and talking on the phone, and walking and listening to music. Variability of the hip (p λ_S = .015, λ_L = .043) and pelvis (p λ_S = .039, λ_L = .017) joint sagittal angles significantly increased when the participants walked and looked at the phone, either in normal or in low-light conditions. No significant difference was observed in the variability of the centre of mass position and muscle activation patterns. When individuals walk and look at the phone screen, the hip and knee joints are constantly trying to adopt a new angle to regulate and maintain gait stability, which might put an additional strain on the neuromuscular system. To this end, it is recommended not to look at the mobile phone screen while walking, particularly in public places with higher risks of falls.