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

Dynamics of Remote Communication: Movement Coordination in Video-Mediated and Face-to-Face Conversations

The present pandemic forced our daily interactions to move into the virtual world. People had to adapt to new communication media that afford different ways of interaction. Remote communication decreases the availability and salience of some cues but also may enable and highlight others. Importantly, basic movement dynamics, which are crucial for any interaction as they are responsible for the informational and affective coupling, are affected. It is therefore essential to discover exactly how these dynamics change. In this exploratory study of six interacting dyads we use traditional variability measures and cross recurrence quantification analysis to compare the movement coordination dynamics in quasi-natural dialogues in four situations: (1) remote video-mediated conversations with a self-view mirror image present, (2) remote video-mediated conversations without a self-view, (3) face-to-face conversations with a self-view, and (4) face-to-face conversations without a self-view. We discovered that in remote interactions movements pertaining to communicative gestures were exaggerated, while the stability of interpersonal coordination was greatly decreased. The presence of the self-view image made the gestures less exaggerated, but did not affect the coordination. The dynamical analyses are helpful in understanding the interaction processes and may be useful in explaining phenomena connected with video-mediated communication, such as “Zoom fatigue”.

Concurrent Effects between Geomagnetic Storms and Magnetospheric Substorms

An accurate understanding of dissimilarities in geomagnetic variability between quiet and disturbed periods has the potential to vastly improve space weather diagnosis. In this work, we exploit some recently developed methods of dynamical system theory to provide new insights and conceptual ideas in space weather science. In particular, we study the co-variation and recurrence statistics of two geomagnetic indices, SYM-H and AL, that measure the intensity of the globally symmetric component of the equatorial electrojet and that of the westward auroral electrojet, respectively. We find that the number of active degrees of freedom, required to describe the phase space dynamics of both indices, depends on the geomagnetic activity level. When the magnetospheric substorm activity, as monitored by the AL index, increases, the active number of degrees of freedom increases at high latitudes above the dimension obtained through classical time delay embedding methods. Conversely, a reduced number of degrees of freedom is observed during geomagnetic storms at low latitude by analysing the SYM-H index. By investigating time-dependent relations between both indices we find that a significant amount of information is shared between high and low latitude current systems originating from coupling mechanisms within the magnetosphere–ionosphere system as the result of a complex interplay between processes and phenomena of internal origin activated by the triggering of external source processes. Our observations support the idea that the near-Earth electromagnetic environment is a complex system far from an equilibrium.

Multiband Spectrum Sensing Based on the Sample Entropy

Cognitive radios represent a real alternative to the scarcity of the radio spectrum. One of the primary tasks of these radios is the detection of possible gaps in a given bandwidth used by licensed users (called also primary users). This task, called spectrum sensing, requires high precision in determining these gaps, maximizing the probability of detection. The design of spectrum sensing algorithms also requires innovative hardware and software solutions for real-time implementations. In this work, a technique to determine possible primary users’ transmissions in a wide frequency interval (multiband spectrum sensing) from the perspective of cognitive radios is presented. The proposal is implemented in a real wireless communications environment using low-cost hardware considering the sample entropy as a decision rule. To validate its feasibility for real-time implementation, a simulated scenario was first tested. Simulation and real-time implementations results were compared with the Higuchi fractal dimension as a decision rule. The encouraging results show that sample entropy correctly detects noise or a possible primary user transmission, with a probability of success around 0.99, and the number of samples with errors at the start and end of frequency edges of transmissions is, on average, only 12 samples.

Recurrence analysis of friction based dry-couplant ultrasonic Lamb waves in plate-like structures

In this study, the effect of friction on the generation of dry-coupled Lamb waves is experimentally investigated. Recurrence analysis is performed to analyze the complex behavior of friction based dry-coupled Lamb waves. In particular, the effect of the normal force, which is necessary for a stronger dry-coupled Lamb wave generation and the friction, on the transmission of mechanical energy and determinism characteristics of Lamb waves are investigated. The results verify that larger friction coefficient and friction force are crucial for generation and propagation of strong Lamb waves supporting the fact that the main mechanism to transfer mechanical energy using dry-couplant is friction. The sensitivity of Lamb waves to the friction coefficient, highlights the importance of designing specific pads with respect to condition of the surface. Besides, the results show that the normal force and friction coefficient can change the determinism characteristics behavior of multimode Lamb waves. Furthermore, it is shown that the determinism value is sensitive to the friction coefficient and normal force. A similar trend is observed in the determinism values and friction coefficient. In general, a smaller friction coefficient indicates smaller determinism value. Additionally, it is shown that a normal load can change the behavior of a system, as observed from recurrence plots, owing to changes in the Lamb waves trajectories in the phase-space domain. In addition, it is shown that recurrence plots enable the detection of mode transitions in multimode Lamb waves. Recurrence analysis is a complementary tool to frequency domain methods for accurate analysis of multimode Lamb waves behavior.

Anticipating synchrony in dynamical systems using information theory

Synchronization in coupled dynamical systems has been a well-known phenomenon in the field of nonlinear dynamics for a long time. This phenomenon has been investigated extensively both analytically and experimentally. Although synchronization is observed in different areas of our real life, in some cases, this phenomenon is harmful; consequently, an early warning of synchronization becomes an unavoidable requirement. This paper focuses on this issue and proposes a reliable measure ( R), from the perspective of the information theory, to detect complete and generalized synchronizations early in the context of interacting oscillators. The proposed measure R is an explicit function of the joint entropy and mutual information of the coupled oscillators. The applicability of R to anticipate generalized and complete synchronizations is justified using numerical analysis of mathematical models and experimental data. Mathematical models involve the interaction of two low-dimensional, autonomous, chaotic oscillators and a network of coupled Rössler and van der Pol oscillators. The experimental data are generated from laboratory-scale turbulent thermoacoustic systems.

Mixed-Precision Kernel Recursive Least Squares

Kernel recursive least squares (KRLS) is a widely used online machine learning algorithm for time series predictions. In this article, we present the mixed-precision KRLS, producing equivalent prediction accuracy to double-precision KRLS with a higher training throughput and a lower memory footprint. The mixed-precision KRLS applies single-precision arithmetic to the computation components being not only numerically resilient but also computationally intensive. Our mixed-precision KRLS demonstrates the 1.32, 1.15, 1.29, 1.09, and 1.08× training throughput improvements using 24.95%, 24.74%, 24.89%, 24.48%, and 24.20% less memory footprint without losing any prediction accuracy compared to double-precision KRLS for a 3-D nonlinear regression, a Lorenz chaotic time series, a Mackey-Glass chaotic time series, a sunspot number time series, and a sea surface temperature time series, respectively.

Multiscale Weighted Permutation Entropy Analysis of Schizophrenia Magnetoencephalograms

Schizophrenia is a neuropsychiatric disease that affects the nonlinear dynamics of brain activity. The primary objective of this study was to explore the complexity of magnetoencephalograms (MEG) in patients with schizophrenia. We combined a multiscale method and weighted permutation entropy to characterize MEG signals from 19 schizophrenia patients and 16 healthy controls. When the scale was larger than 42, the MEG signals of schizophrenia patients were significantly more complex than those of healthy controls (p<0.004). The difference in complexity between patients with schizophrenia and the controls was strongest in the frontal and occipital areas (p<0.001), and there was almost no difference in the central area. In addition, the results showed that the dynamic range of MEG complexity is wider in healthy individuals than in people with schizophrenia. Overall, the multiscale weighted permutation entropy method reliably quantified the complexity of MEG from schizophrenia patients, contributing to the development of potential magnetoencephalographic biomarkers for schizophrenia.

Network Analysis of Time Series: Novel Approaches to Network Neuroscience

In the last two decades, there has been an explosion of interest in modeling the brain as a network, where nodes correspond variously to brain regions or neurons, and edges correspond to structural or statistical dependencies between them. This kind of network construction, which preserves spatial, or structural, information while collapsing across time, has become broadly known as "network neuroscience." In this work, we provide an alternative application of network science to neural data: network-based analysis of non-linear time series and review applications of these methods to neural data. Instead of preserving spatial information and collapsing across time, network analysis of time series does the reverse: it collapses spatial information, instead preserving temporally extended dynamics, typically corresponding to evolution through some kind of phase/state-space. This allows researchers to infer a, possibly low-dimensional, "intrinsic manifold" from empirical brain data. We will discuss three methods of constructing networks from nonlinear time series, and how to interpret them in the context of neural data: recurrence networks, visibility networks, and ordinal partition networks. By capturing typically continuous, non-linear dynamics in the form of discrete networks, we show how techniques from network science, non-linear dynamics, and information theory can extract meaningful information distinct from what is normally accessible in standard network neuroscience approaches.

Largest Lyapunov Exponent Optimization for Control of a Bionic-Hand: A Brain Computer Interface Study

This paper introduces a brain control bionic-hand, and several methods have been developed for predicting and quantifying the behavior of a non-linear system such as a brain. Non-invasive investigations on the brain were conducted by means of electroencephalograph (EEG) signal oscillations. One of the prominent concepts necessary to understand EEG signals is the chaotic concept named the fractal dimension and the largest Lyapunov exponent (LLE). Specifically, the LLE algorithm called the chaotic quantifier method has been employed to compute the complexity of a system. The LLE helps us to understand how the complexity of the brain changes while making a decision to close and open a fist. The LLE has been used for a long time, but here we optimize the traditional LLE algorithm to attain higher accuracy and precision for controlling a bionic hand. In the current study, the main constant input parameters of the LLE, named the false nearest neighbor and mutual information, are parameterized and then optimized by means of the Water Drop (WD) and Chaotic Tug of War (CTW) optimizers. The optimized LLE is then employed to identify imaginary movement patterns from the EEG signals for control of a bionic hand. The experiment includes 21 subjects for recording imaginary patterns. The results illustrated that the CTW solution achieved a higher average accuracy rate of 72.31% in comparison to the traditional LLE and optimized LLE by using a WD optimizer. The study concluded that the traditional LLE required enhancement using optimization methods. In addition, the CTW approximation method has the potential for more efficient solutions in comparison to the WD method.

Balance on different unstable supports: a complementary approach based on linear and non-linear analyses

Maintenance of postural control is a complex task that requires the integration of different sensory-motor processes. To improve postural control, balance training is often implemented using unstable surfaces. Little is known, however, about how different surfaces compare in terms of postural control strategy. Non-linear dynamical system analysis, like recurrent quantification analysis (RQA) applied to the center of pressure (CoP) trajectory, represents a useful tool in this respect. The aim of this study is to investigate the effects of different unstable supports on the CoP trajectory through a complementary approach based on linear and non-linear analyses. Seventeen healthy adults performed barefoot single-leg balance trials on a force plate and on three different balance training devices (soft disc, foam pad, and pillow). Sets of parameters were extracted from the CoP trajectories using classical stabilometric analysis (sway path, mean velocity, root mean square) and RQA (percent recurrence and determinism, maximum line length, entropy). Both classical and RQA analyses highlighted significant differences between stable (force plate) and unstable conditions (p < 0.001). Conversely, only classical stabilometric parameters showed significant differences among the considered balance training devices, indicating that the different characteristics of the devices do not influence the dynamic/temporal structure of the CoP trajectory. Analysis of the center of pressure trajectory during single-leg standing on three different balance training devices and on a rigid surface using both linear and non-linear techniques.

Tangle: A metric for quantifying complexity and erratic behavior in short time series

Temporal complexity refers to qualities of a time series that are emergent, erratic, or not easily described by linear processes. Quantifying temporal complexity within a system is key to understanding the time based dynamics of said system. However, many current methods of complexity quantification are not widely used in psychological research because of their technical difficulty, computational intensity, or large number of required data samples. These requirements impede the study of complexity in many areas of psychological science. A method is presented, tangle, which overcomes these difficulties and allows for complexity quantification in relatively short time series, such as those typically obtained from psychological studies. Tangle is a measure of how dissimilar a given process is from simple periodic motion. Tangle relies on the use of a three-dimensional time delay embedding of a one-dimensional time series. This embedding is then iteratively scaled and premultiplied by a modified upshift matrix until a convergence criterion is reached. The efficacy of tangle is shown on five mathematical time series and using emotional stability, anxiety time series data obtained from 65 socially anxious participants over a 5-week period, and positive affect time series derived from a single participant who experienced a major depression episode during measurement. Simulation results show tangle is able to distinguish between different complex temporal systems in time series with as few as 50 samples. Tangle shows promise as a reliable quantification of irregular behavior of a time series. Unlike many other complexity quantification metrics, tangle is technically simple to implement and is able to uncover meaningful information about time series derived from psychological research studies. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Nonlinear causal analysis reveals an effective water level regulation approach for phytoplankton blooms controlling in reservoirs

Reservoirs are a rapidly increasing water body providing water supply, irrigation, and many other benefits for human societies globally. However, due to changes in hydrological conditions, building reservoirs tends to bring adverse effects such as eutrophication and phytoplankton blooms, reducing the ecosystem service values. This study focuses on using the empirical dynamic modeling (EDM), an emerging approach for nonlinear analysis, to investigate the nonlinear causal relationship of water level fluctuation (WLF) on phytoplankton biomass and then develop a quantitative model guiding effective phytoplankton blooms controlling based on water level regulations in reservoirs. Specifically, with 9-year continued daily observed data in the Three Gorges Reservoir, we examined the causal effects of different WLF parameters on the dynamics of phytoplankton blooms for the first time. We found that the water level change in the past 24 h (ΔWL) has the strongest causal effect on the daily dynamics of phytoplankton biomass among all WLF parameters (ΔWL, |ΔWL|, and the water level), with a time lag of 2 days. Moreover, EDM revealed a nonlinear relationship between ΔWL and daily dynamics of phytoplankton biomass and achieved a successful prediction for the chlorophyll a concentration 2-day ahead. Further scenario analyses found that both the rise and fall of water level will significantly reduce the chlorophyll a concentration when phytoplankton blooms occur. Nevertheless, on the whole, the rising water level has a more substantial effect on phytoplankton blooms than falling the water level. This result reveals that regulating ΔWL is a simple and effective approach in controlling phytoplankton blooms in reservoirs. Our study reported the nonlinear causal effect of ΔWL on the dynamics of chlorophyll a and provided a quantitative approach guiding effective phytoplankton blooms controlling based on the water level regulation, which might have a broad application in algal blooms controlling in reservoirs and similar waterbodies.

Effects of task prioritization on a postural-motor task in early-stage Parkinson's disease: EEG connectivity and clinical implication

Appropriate attentional resource allocation could minimize exaggerated dual-task interference due to basal ganglia dysfunction in Parkinson's disease (PD). Here, we assessed the electroencephalography (EEG) functional connectivity to investigate how task prioritization affected posture-motor dual-tasks in PD. Sixteen early-stage PD patients and 16 healthy controls maintained balance in narrow stance alone (single-posture task) or while separating two interlocking rings (postural dual-task). The participants applied a posture-focus or supraposture-focus strategy in the postural dual-task. Postural sway dynamics, ring-touching time, and scalp EEG were analyzed. Both groups exhibited smaller postural sway size, postural determinism, and ring-touching time with the supraposture-focus versus posture-focus strategy. PD patients exhibited higher mean inter-regional connectivity strength than control subjects in both single and dual-task postural conditions. To cope with dual-task interference, PD patients increased inter-regional connectivity (especially with the posture-focus strategy), while control subjects reduced inter-regional connectivity. The difference in mean connectivity strength between the dual-task condition with supraposture-focus and single-posture condition was negatively correlated to the Movement Disorder Society Unified Parkinson's Disease Rating Scale (MDS-UPDRS) part III total scores and hand-related sub-scores. Our findings suggest differential task prioritization effects on dual-task performance and cortical reorganization between early-stage PD and healthy individuals. Early-stage PD patients are advocated to use a supraposture-focus strategy during a postural dual-task. In addition, with a supraposture-focus strategy, PD patients with mild motor severity could increase compensatory inter-regional connectivity to cope with dual-task interference.

Phenomenological Model of Nonlinear Dynamics and Deterministic Chaotic Gas Migration in Bentonite: Experimental Evidence and Diagnostic Parameters

Understanding gas migration in compacted clay materials, e.g., bentonite and claystone, is important for the design and performance assessment of an engineered barrier system of a radioactive waste repository system, as well as many practical applications. Existing field and laboratory data on gas migration processes in low-permeability clay materials demonstrate the complexity of flow and transport processes, including various types of instabilities, caused by nonlinear dynamics of coupled processes of liquid–gas exchange, dilation, fracturing, fracture healing, etc., which cannot be described by classical models of fluid dynamics in porous media. We here show that the complexity of gas migration processes can be explained using a phenomenological concept of nonlinear dynamics and deterministic chaos theory. To do so, we analyzed gas pressure and gas influx (i.e., input) and outflux (i.e., output), recorded during the gas injection experiment in the compact Mx80-D bentonite sample, and calculated a set of the diagnostic parameters of nonlinear dynamics and chaos, such a global embedding dimension, a correlation dimension, an information dimension, and a spectrum of Lyapunov exponents, as well as plotted 2D and 3D pseudo-phase-space strange attractors, based on the univariate influx and outflux time series data. These results indicate the presence of phenomena of low-dimensional deterministic chaotic behavior of gas migration in bentonite. In particular, during the onset of gas influx in the bentonite core, before the breakthrough, the development of gas flow pathways is characterized by the process of chaotic gas diffusion. After the breakthrough, with inlet-to-outlet movement of gas, the prevailing process is chaotic advection. During the final phase of the experiment, with no influx to the sample, the relaxation pattern of gas outflux is resumed back to a process of chaotic diffusion. The types of data analysis and a proposed phenomenological model can be used to establish the basic principles of experimental data-gathering, modeling predictions, and a research design.

Recurrence analysis of sensorimotor trajectories in a minimalist perceptual task using sonification

Active Perception perspectives claim that action is closely related to perception. An empirical approach that supports these theories is the minimalist, in which participants perform a task using an interface that provides minimal information. Their exploratory movements are crucial to generating a meaningful sequence of information. Previous studies analyzed sensorimotor trajectories describing qualitative strategies and linear quantification of participants' movement performance, but that approach struggles to capture the behavior of non-stationary data. In the present study, we applied the recurrence plot (RP) and recurrence quantification analysis (RQA) to study the structure of sensorimotor trajectories developed by participants trying to discriminate between two invisible geometric shapes (Triangle or Rectangle). The exploratory movements were made using a computer mouse and sonification-mediated feedback was provided, which depended exclusively on whether the pointer was inside or outside the shape. We applied RP and RQA to the sensorimotor trajectories, with the aim of studying their fine structure characteristics, focusing on their repetitive patterns. Recurrence analysis proved to be useful for quantifying differences in dynamic behavior that emerge when participants explore invisible virtual geometric shapes. The differences obtained in RQA-based measures associated with the vertical structures allowed to postulate the existence of particular exploration strategies for each figure. It was also possible to determine that the complexity of the dynamics changed according to the shape. We discuss these results in light of antecedents in haptic and visual perceptual exploration.

Computational Approaches and Tools as Applied to the Study of Rhythms and Chaos in Biology

The temporal dynamics in biological systems displays a wide range of behaviors, from periodic oscillations, as in rhythms, bursts, long-range (fractal) correlations, chaotic dynamics up to brown and white noise. Herein, we propose a comprehensive analytical strategy for identifying, representing, and analyzing biological time series, focusing on two strongly linked dynamics: periodic (oscillatory) rhythms and chaos. Understanding the underlying temporal dynamics of a system is of fundamental importance; however, it presents methodological challenges due to intrinsic characteristics, among them the presence of noise or trends, and distinct dynamics at different time scales given by molecular, dcellular, organ, and organism levels of organization. For example, in locomotion circadian and ultradian rhythms coexist with fractal dynamics at faster time scales. We propose and describe the use of a combined approach employing different analytical methodologies to synergize their strengths and mitigate their weaknesses. Specifically, we describe advantages and caveats to consider for applying probability distribution, autocorrelation analysis, phase space reconstruction, Lyapunov exponent estimation as well as different analyses such as harmonic, namely, power spectrum; continuous wavelet transforms; synchrosqueezing transform; and wavelet coherence. Computational harmonic analysis is proposed as an analytical framework for using different types of wavelet analyses. We show that when the correct wavelet analysis is applied, the complexity in the statistical properties, including temporal scales, present in time series of signals, can be unveiled and modeled. Our chapter showcase two specific examples where an in-depth analysis of rhythms and chaos is performed: (1) locomotor and food intake rhythms over a 42-day period of mice subjected to different feeding regimes; and (2) chaotic calcium dynamics in a computational model of mitochondrial function.

Complexity of COVID-19 Dynamics

With population explosion and globalization, the spread of infectious diseases has been a major concern. In 2019, a newly identified type of Coronavirus caused an outbreak of respiratory illness, popularly known as COVID-19, and became a pandemic. Although enormous efforts have been made to understand the spread of COVID-19, our knowledge of the COVID-19 dynamics still remains limited. The present study employs the concepts of chaos theory to examine the temporal dynamic complexity of COVID-19 around the world. The false nearest neighbor (FNN) method is applied to determine the dimensionality and, hence, the complexity of the COVID-19 dynamics. The methodology involves: (1) reconstruction of a single-variable COVID-19 time series in a multi-dimensional phase space to represent the underlying dynamics; and (2) identification of “false” neighbors in the reconstructed phase space and estimation of the dimension of the COVID-19 series. For implementation, COVID-19 data from 40 countries/regions around the world are studied. Two types of COVID-19 data are analyzed: (1) daily COVID-19 cases; and (2) daily COVID-19 deaths. The results for the 40 countries/regions indicate that: (1) the dynamics of COVID-19 cases exhibit low- to medium-level complexity, with dimensionality in the range 3 to 7; and (2) the dynamics of COVID-19 deaths exhibit complexity anywhere from low to high, with dimensionality ranging from 3 to 13. The results also suggest that the complexity of the dynamics of COVID-19 deaths is greater than or at least equal to that of the dynamics of COVID-19 cases for most (three-fourths) of the countries/regions. These results have important implications for modeling and predicting the spread of COVID-19 (and other infectious diseases), especially in the identification of the appropriate complexity of models.

Non-linear Methods Predominant in Fetal Heart Rate Analysis: A Systematic Review

The analysis of fetal heart rate variability has served as a scientific and diagnostic tool to quantify cardiac activity fluctuations, being good indicators of fetal well-being. Many mathematical analyses were proposed to evaluate fetal heart rate variability. We focused on non-linear analysis based on concepts of chaos, fractality, and complexity: entropies, compression, fractal analysis, and wavelets. These methods have been successfully applied in the signal processing phase and increase knowledge about cardiovascular dynamics in healthy and pathological fetuses. This review summarizes those methods and investigates how non-linear measures are related to each paper's research objectives. Of the 388 articles obtained in the PubMed/Medline database and of the 421 articles in the Web of Science database, 270 articles were included in the review after all exclusion criteria were applied. While approximate entropy is the most used method in classification papers, in signal processing, the most used non-linear method was Daubechies wavelets. The top five primary research objectives covered by the selected papers were detection of signal processing, hypoxia, maturation or gestational age, intrauterine growth restriction, and fetal distress. This review shows that non-linear indices can be used to assess numerous prenatal conditions. However, they are not yet applied in clinical practice due to some critical concerns. Some studies show that the combination of several linear and non-linear indices would be ideal for improving the analysis of the fetus's well-being. Future studies should narrow the research question so a meta-analysis could be performed, probing the indices' performance.

De-Noising of Magnetotelluric Signals by Discrete Wavelet Transform and SVD Decomposition

Magnetotelluric (MT) sounding data can easily be damaged by various types of noise, especially in industrial areas, where the quality of measured data is poor. Most traditional de-noising methods are ineffective to the low signal-to-noise ratio of data. To solve the above problem, we propose the use of a de-noising method for the detection of noise in MT data based on discrete wavelet transform and singular value decomposition (SVD), with multiscale dispersion entropy and phase space reconstruction carried out for pretreatment. No “over processing” takes place in the proposed method. Compared with wavelet transform and SVD decomposition in synthetic tests, the proposed method removes the profile of noise more completely, including large-scale noise and impulse noise. For high levels or low levels of noise, the proposed method can increase the signal-to-noise ratio of data more obviously. Moreover, application to the field MT data can prove the performance of the proposed method. The proposed method is a feasible method for the elimination of various noise types and can improve MT data with high noise levels, obtaining a recovery in the response. It can improve abrupt points and distortion in MT response curves more effectively than the robust method can.

Classification of Chaotic Squeak and Rattle Vibrations by CNN Using Recurrence Pattern

The chaotic squeak and rattle (S&R) vibrations in mechanical systems were classified by deep learning. The rattle, single-mode, and multi-mode squeak models were constructed to generate chaotic S&R signals. The repetition of nonlinear signals generated by them was visualized using an unthresholded recurrence plot and learned using a convolutional neural network (CNN). The results showed that even if the signal of the S&R model is chaos, it could be classified. The accuracy of the classification was verified by calculating the Lyapunov exponent of the vibration signal. The numerical experiment confirmed that the CNN classification using nonlinear vibration images as the proposed procedure has more than 90% accuracy. The chaotic status and each model can be classified into six classes.

Toward automated extraction and characterization of scaling regions in dynamical systems

Scaling regions-intervals on a graph where the dependent variable depends linearly on the independent variable-abound in dynamical systems, notably in calculations of invariants like the correlation dimension or a Lyapunov exponent. In these applications, scaling regions are generally selected by hand, a process that is subjective and often challenging due to noise, algorithmic effects, and confirmation bias. In this paper, we propose an automated technique for extracting and characterizing such regions. Starting with a two-dimensional plot-e.g., the values of the correlation integral, calculated using the Grassberger-Procaccia algorithm over a range of scales-we create an ensemble of intervals by considering all possible combinations of end points, generating a distribution of slopes from least squares fits weighted by the length of the fitting line and the inverse square of the fit error. The mode of this distribution gives an estimate of the slope of the scaling region (if it exists). The end points of the intervals that correspond to the mode provide an estimate for the extent of that region. When there is no scaling region, the distributions will be wide and the resulting error estimates for the slope will be large. We demonstrate this method for computations of dimension and Lyapunov exponent for several dynamical systems and show that it can be useful in selecting values for the parameters in time-delay reconstructions.

Effect of combining features generated through non-linear analysis and wavelet transform of EEG signals for the diagnosis of encephalopathy

Electroencephalogram (EEG) signals portray hidden neuronal interactions in the brain and indicate brain dynamics. These signals are dynamic, complex, chaotic and nonlinear, the nature of which is represented with features - fractal dimensions, entropies and chaotic features. This study aims at examining the discriminative power of individual features and their combination in the diagnosis of a neuro-pathological condition called encephalopathy. Feature combination is accomplished with the help of feature selection using Gini impurity score that improves discriminative power and keeps redundancy minimal. Further, three widely used non-parametric classifiers which are known to be effective with wavelet features on EEG signals - Support Vector Machine, Random Forest, Multilayer Perceptron - are employed for disease classification. The models created by the combination of aforementioned stages are analysed and evaluated with performance scores, leading to an optimal model for automated diagnostic applications.

The Deterministic Nature of Sensor-Based Information for Condition Monitoring of the Cutting Process

Condition monitoring of the cutting process is a core function of autonomous machining and its success strongly relies on sensed data. Despite the enormous amount of research conducted so far into condition monitoring of the cutting process, there are still limitations given the complexity underlining tool wear; hence, a clearer understanding of sensed data and its dynamical behavior is fundamental to sustain the development of more robust condition monitoring systems. The dependence of these systems on acquired data is critical and determines the success of such systems. In this study, data is acquired from an experimental setup using some of the commonly used sensors for condition monitoring, reproducing realistic cutting operations, and then analyzed upon their deterministic nature using different techniques, such as the Lyapunov exponent, mutual information, attractor dimension, and recurrence plots. The overall results demonstrate the existence of low dimensional chaos in both new and worn tools, defining a deterministic nature of cutting dynamics and, hence, broadening the available approaches to tool wear monitoring based on the theory of chaos. In addition, recurrence plots depict a clear relationship to tool condition and may be quantified considering a two-dimensional structural measure, such as the semivariance. This exploratory study unveils the potential of non-linear dynamics indicators in validating information strength potentiating other uses and applications.

Detecting Epileptic Seizures via Non-Uniform Multivariate Embedding of EEG Signals

Efficient real-time detection of epileptic seizures remains a challenging task in clinical practice. In this study, we introduce a new thresholding method to monitor brain activities via a non-uniform multivariate (NUM) embedding of multi-channel electroencephalogram (EEG) signals. Specifically, we present a NUM embedding optimization problem to identify the best embedding parameters. We originate one feature, named non-uniform multivariate multiscale entropy (NUMME), which is extracted from the NUM embedded EEG data. Finally, the extracted feature, compared to an individualized threshold, is used for monitoring and detecting seizure onsets. Experimental results on the real CHB-MIT Scalp EEG database show that our approach achieves a comparable performance to the state-of-art methods. Moreover, it is important to note that we accomplish this without using any sophisticated machine learning algorithms.

Different unilateral force control strategies between athletes and non-athletes

This study investigated continuous visuomotor tracking capabilities between athletes and non-athlete controls using isometric force control paradigm. Nine female athletes and nine female age-matched controls performed unilateral hand-grip force control tasks with their dominant and non-dominant hands at 10% and 40% of maximal voluntary contraction (MVC), respectively. Three conventional outcome measures on force control capabilities included mean force, force accuracy, and force variability, and we additionally calculated two nonlinear dynamics variables including force regularity using sample entropy and force stability using maximal Lyapunov exponent. Finally, we performed correlation analyses to determine the relationship between nonlinear dynamics variables and conventional measures for each group. The findings indicated that force control capabilities as indicated by three conventional measures were not significantly different between athlete and non-athlete control groups. However, the athletes revealed less force regularity and greater force stability across hand conditions and targeted force levels than those in non-athlete controls. The correlation analyses found that increased force regularity (i.e., less sample entropy values) at 10% of MVC and decreased force regularity (i.e., greater sample entropy values) at 40% of MVC were significantly related to improved force accuracy and variability for the athlete group, and these patterns were not observed in the non-athlete control group. These findings suggested that the athletes may use different adaptive force control strategies as indicated by nonlinear dynamics tools.

Electrocorticography reveals thalamic control of cortical dynamics following traumatic brain injury

The return of consciousness after traumatic brain injury (TBI) is associated with restoring complex cortical dynamics; however, it is unclear what interactions govern these complex dynamics. Here, we set out to uncover the mechanism underlying the return of consciousness by measuring local field potentials (LFP) using invasive electrophysiological recordings in patients recovering from TBI. We found that injury to the thalamus, and its efferent projections, on MRI were associated with repetitive and low complexity LFP signals from a highly structured phase space, resembling a low-dimensional ring attractor. But why do thalamic injuries in TBI patients result in a cortical attractor? We built a simplified thalamocortical model, which connotes that thalamic input facilitates the formation of cortical ensembles required for the return of cognitive function and the content of consciousness. These observations collectively support the view that thalamic input to the cortex enables rich cortical dynamics associated with consciousness.

Reconstructing large interaction networks from empirical time series data

Reconstructing interactions from observational data is a critical need for investigating natural biological networks, wherein network dimensionality is usually high. However, these pose a challenge to existing methods that can quantify only small interaction networks. Here, we proposed a novel approach to reconstruct high-dimensional interaction Jacobian networks using empirical time series without specific model assumptions. This method, named "multiview distance regularised S-map," generalised the state space reconstruction to accommodate high dimensionality and overcome difficulties in quantifying massive interactions with limited data. When evaluating this method using time series generated from theoretical models involving hundreds of interacting species, estimated strengths of interaction Jacobians were in good agreement with theoretical expectations. Applying this method to a natural bacterial community helped identify important species from the interaction network and revealed mechanisms governing the dynamical stability of a bacterial community. The proposed method overcame the challenge of high dimensionality in large natural dynamical systems.

Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations

We present a supervised learning method to learn the propagator map of a dynamical system from partial and noisy observations. In our computationally cheap and easy-to-implement framework, a neural network consisting of random feature maps is trained sequentially by incoming observations within a data assimilation procedure. By employing Takens's embedding theorem, the network is trained on delay coordinates. We show that the combination of random feature maps and data assimilation, called RAFDA, outperforms standard random feature maps for which the dynamics is learned using batch data.

Nonlinear recurrence quantification of the monsoon-season heavy rainy-days over northwest Himalaya for the baseline and future periods

Indian summer monsoon has the characteristics of nonlinear dynamical systems. This study verifies the hypothesis that monsoon-season heavy rainy-day climatology over northwest Himalaya would exhibit certain degree of determinism, and expected to modify in its future state due to warming. Hence, recurrence quantification analysis (RQA) leading to quantification of recurrence rate (RR) and determinism (DET) are used. The monsoon-season heavy rainy-day climatologies are computed by area averaging heavy rainy-day (i.e. any day having rainfall ≥35.5 mm) of northwestern Indian Himalaya of Uttarakhand (UK), Himachal Pradesh (HP), and Union Territory of Jammu, Kashmir and Ladakh (JKL). Nonlinear characteristics are identified for a baseline period of 1970-2005 using APHRODITE data, and a bias corrected ensemble data for the future period of 2041-2099 produced using five CORDEX experiments under two warming scenarios, RCP 4.5 and 8.5. The heavy rainy-day climatology during 1970-2005 is having a correlation dimension of 1.5 indicating fractal geometry of the system in phase space. Similarly, occurrences of diagonal lines in the recurrence plots of baseline period over JKL, HP, and UK indicated the system is governed by a nonlinear chaotic attractor. A higher recurrence rate during 1970-2005 over HP (RR = 0.123, DET = 0.83) indicated greater determinism than JKL (RR = 0.119, DET = 0.78) and UK (RR = 0.121, DET = 0.75). Mean prediction time of the nonlinear dynamical trajectories controlling heavy rainy-day climatology of 1970-2005 is noted to be higher over UK. Furthermore, the RQA patterns under warmer climates of RCP 4.5 and 8.5 during 2041-2099 over UK and JKL indicate gradual reduction in the deterministic structures in the phase space. Therefore, it can be inferred that the nonlinear dynamical system governing the monsoon-season heavy rainy-day climatology is expected to lose determinism over certain regions of northwestern Himalaya under warmer climates of RCP 4.5 and 8.5.

Effects of ECG Data Length on Heart Rate Variability among Young Healthy Adults

The relationship between the robustness of HRV derived by linear and nonlinear methods to the required minimum data lengths has yet to be well understood. The normal electrocardiography (ECG) data of 14 healthy volunteers were applied to 34 HRV measures using various data lengths, and compared with the most prolonged (2000 R peaks or 750 s) by using the Mann-Whitney U test, to determine the 0.05 level of significance. We found that SDNN, RMSSD, pNN50, normalized LF, the ratio of LF and HF, and SD1 of the Poincaré plot could be adequately computed by small data size (60-100 R peaks). In addition, parameters of RQA did not show any significant differences among 60 and 750 s. However, longer data length (1000 R peaks) is recommended to calculate most other measures. The DFA and Lyapunov exponent might require an even longer data length to show robust results. Conclusions: Our work suggests the optimal minimum data sizes for different HRV measures which can potentially improve the efficiency and save the time and effort for both patients and medical care providers.

Effect of gravity on synchronization of two coupled buoyancy-induced turbulent flames

We study the effect of gravity on the synchronization of two coupled buoyancy-induced turbulent flames by recurrence-based analysis and machine learning. A significant change from nearly complete synchronization in the near field to partial synchronization appears in the far field under low gravity. The synchronized state is gradually lost with increasing gravity level. These results are clearly identified from cross recurrence plots and symbolic recurrence plots and by reservoir computing.

A General Metric for the Similarity of Both Stochastic and Deterministic System Dynamics

Many problems in the study of dynamical systems—including identification of effective order, detection of nonlinearity or chaos, and change detection—can be reframed in terms of assessing the similarity between dynamical systems or between a given dynamical system and a reference. We introduce a general metric of dynamical similarity that is well posed for both stochastic and deterministic systems and is informative of the aforementioned dynamical features even when only partial information about the system is available. We describe methods for estimating this metric in a range of scenarios that differ in respect to contol over the systems under study, the deterministic or stochastic nature of the underlying dynamics, and whether or not a fully informative set of variables is available. Through numerical simulation, we demonstrate the sensitivity of the proposed metric to a range of dynamical properties, its utility in mapping the dynamical properties of parameter space for a given model, and its power for detecting structural changes through time series data.

Biometric Identification Based on Eye Movement Dynamic Features

The paper presents studies on biometric identification methods based on the eye movement signal. New signal features were investigated for this purpose. They included its representation in the frequency domain and the largest Lyapunov exponent, which characterizes the dynamics of the eye movement signal seen as a nonlinear time series. These features, along with the velocities and accelerations used in the previously conducted works, were determined for 100-ms eye movement segments. 24 participants took part in the experiment, composed of two sessions. The users’ task was to observe a point appearing on the screen in 29 locations. The eye movement recordings for each point were used to create a feature vector in two variants: one vector for one point and one vector including signal for three consecutive locations. Two approaches for defining the training and test sets were applied. In the first one, 75% of randomly selected vectors were used as the training set, under a condition of equal proportions for each participant in both sets and the disjointness of the training and test sets. Among four classifiers: kNN (k = 5), decision tree, naïve Bayes, and random forest, good classification performance was obtained for decision tree and random forest. The efficiency of the last method reached 100%. The outcomes were much worse in the second scenario when the training and testing sets when defined based on recordings from different sessions; the possible reasons are discussed in the paper.

Unsupervised quantification of naturalistic animal behaviors for gaining insight into the brain

Neural computation has evolved to optimize the behaviors that enable our survival. Although much previous work in neuroscience has focused on constrained task behaviors, recent advances in computer vision are fueling a trend toward the study of naturalistic behaviors. Automated tracking of fine-scale behaviors is generating rich datasets for animal models including rodents, fruit flies, zebrafish, and worms. However, extracting meaning from these large and complex data often requires sophisticated computational techniques. Here we review the latest methods and modeling approaches providing new insights into the brain from behavior. We focus on unsupervised methods for identifying stereotyped behaviors and for resolving details of the structure and dynamics of behavioral sequences.

Predicting the effect of confinement on the COVID-19 spread using machine learning enriched with satellite air pollution observations

The real-time monitoring of reductions of economic activity by containment measures and its effect on the transmission of the coronavirus (COVID-19) is a critical unanswered question. We inferred 5,642 weekly activity anomalies from the meteorology-adjusted differences in spaceborne tropospheric NO2 column concentrations after the 2020 COVID-19 outbreak relative to the baseline from 2016 to 2019. Two satellite observations reveal reincreasing economic activity associated with lifting control measures that comes together with accelerating COVID-19 cases before the winter of 2020/2021. Application of the near-real-time satellite NO2 observations produces a much better prediction of the deceleration of COVID-19 cases than applying the Oxford Government Response Tracker, the Public Health and Social Measures, or human mobility data as alternative predictors. A convergent cross-mapping suggests that economic activity reduction inferred from NO2 is a driver of case deceleration in most of the territories. This effect, however, is not linear, while further activity reductions were associated with weaker deceleration. Over the winter of 2020/2021, nearly 1 million daily COVID-19 cases could have been avoided by optimizing the timing and strength of activity reduction relative to a scenario based on the real distribution. Our study shows how satellite observations can provide surrogate data for activity reduction during the COVID-19 pandemic and monitor the effectiveness of containment to the pandemic before vaccines become widely available.

Revealing Sex Differences During Upper and Lower Extremity Neuromuscular Fatigue in Older Adults Through a Neuroergonomics Approach

Background: Sex differences in neuromuscular fatigue is well-documented, however the underlying mechanisms remain understudied, particularly for the aging population. Objective: This study investigated sex differences in fatigability of the upper and lower extremity of older adults using a neuroergonomics approach. Methods: Thirty community-dwelling older adults (65 years or older; 15 M, 15 F) performed intermittent submaximal fatiguing handgrip and knee extension exercises until voluntary exhaustion on separate days. Muscle activity from prime muscles of the hand/arm and knee extensors were monitored using electromyography, neural activity from the frontal, motor, and sensory areas were monitored using functional near infrared spectroscopy, and force output were obtained. Results: While older males were stronger than females across both muscle groups, they exhibited longer endurance times and greater strength loss during knee extension exercises. These lower extremity findings were associated with greater force complexity over time and concomitant increase in left motor and right sensory motor regions. While fatigability during handgrip exercises was comparable across sexes, older females exhibited concurrent increases in the activation of the ipsilateral motor regions over time. Discussion: We identified differences in the underlying central neural strategies adopted by males and females in maintaining downstream motor outputs during handgrip fatigue that were not evident with traditional ergonomics measures. Additionally, enhanced neural activation in males during knee exercises that accompanied longer time to exhaustion point to potential rehabilitation/exercise strategies to improve neuromotor outcomes in more fatigable older adults.

Unsupervised Detection of Anomalies in Fetal Heart Rate Tracings using Phase Space Reconstruction

Detection of anomalies in time series is still a challenging problem. In this paper, we provide a new approach to unsupervised detection of anomalies in time series based on the concept of phase space reconstruction and manifolds. We propose a rotation-insensitive metric for quantifying the similarity of manifolds and a method that uses it for estimating the probability of an outlier. The proposed method does not rely on any features and can be used for signals with variable lengths. We tested it on both synthetic signals and real fetal heart rate tracings. The method has promising performance and can be used for interpreting the severity of fetal asphyxia.

Convolutional neural network analysis of recurrence plots for high resolution melting classification

BACKGROUND AND OBJECTIVE

High resolution melting (HRM) analysis is a rapid and correct method for identification of species, such as, microorganism, bacteria, yeast, virus, etc. HRM data are produced using real-time polymerase chain reaction (PCR) and unique for each species. Analysis of the HRM data is important for several applications, such as, for detection of diseases (e.g., influenza, zika virus, SARS-Cov-2 and Covid-19 diseases) in health, for identification of spoiled foods in food industry, for analysis of crime scene evidence in forensic investigation, etc. However, the characteristics of the HRM data can change due to the experimental conditions or instrumental settings. In addition, it becomes laborious and time-consuming process as the number of samples increases. Because of these reasons, the analysis and classification of the HRM data become challenging for species which have similar characteristics.

METHODS

To improve the classification accuracy of HRM data, we propose to use image (visual) representation of HRM data, which we call HRM images, that are generated using recurrence plots, and propose convolutional neural network (CNN) based models for classifying HRM images. In this study, two different types of recurrence plots are generated, which are black-white recurrence plots (BW-RP) and gray scale recurrence plots (GS-RP) and four different CNN models are proposed for classifying HRM data.

RESULTS

The classification performance of the proposed methods are evaluated based on average classification accuracy and F1 score, specificity, recall, and precision values for each yeast species. When BW-RP representation of HRM data is used as input to the CNN models, the best classification accuracy of 95.2% is obtained. The classification accuracies of CNN models for melting curve and GS-RP data representations of HRM data are 90.13% and 86.13%, respectively. The classification accuracy of support vector machines (SVM) model that take melting curve representation of HRM data is 86.53%. Moreover, when BW-RP representation of HRM data is used as input to the CNN models, the F1 score, specificity, recall and precision values are the highest for almost all of species.

CONCLUSIONS

Experimental results show that using BW-RP representation of HRM data improved the classification accuracy of HRM data and CNN models that take these images as input outperformed CNN models that take melting curve and GS-RP representations of HRM data as inputs and SVM model that take melting curve representation of HRM data as input.

Causality indices for bivariate time series data: A comparative review of performance

Inferring nonlinear and asymmetric causal relationships between multivariate longitudinal data is a challenging task with wide-ranging application areas including clinical medicine, mathematical biology, economics, and environmental research. A number of methods for inferring causal relationships within complex dynamic and stochastic systems have been proposed, but there is not a unified consistent definition of causality in the context of time series data. We evaluate the performance of ten prominent causality indices for bivariate time series across four simulated model systems that have different coupling schemes and characteristics. Pairwise correlations between different methods, averaged across all simulations, show that there is generally strong agreement between methods, with minimum, median, and maximum Pearson correlations between any pair (excluding two similarity indices) of 0.298, 0.719, and 0.955, respectively. In further experiments, we show that these methods are not always invariant to real-world relevant transformations (data availability, standardization and scaling, rounding errors, missing data, and noisy data). We recommend transfer entropy and nonlinear Granger causality as particularly strong approaches for estimating bivariate causal relationships in real-world applications. Both successfully identify causal relationships and a lack thereof across multiple simulations, while remaining robust to rounding errors, at least 20% missing data and small variance Gaussian noise. Finally, we provide flexible open-access Python code for computation of these methods and for the model simulations.

Exploiting Causality for Improved Prediction of Patient Volumes by Gaussian Processes

Estimating and surveillance volumes of patients are of great importance for public health and resource allocation. In many situations, the change of these volumes is correlated with many factors, e.g., seasonal environmental variables, medicine sales, and patient medical claims. It is often of interest to predict patient volumes and to that end, discovering causalities can improve the prediction accuracy. Correlations do not imply causations and they can be spurious, which in turn may entail deterioration of prediction performance if the prediction is based on them. By contrast, in this paper, we propose an approach for prediction based on causalities discovered by Gaussian processes. Our interest is in estimating volumes of patients that suffer from allergy and where the model and the results are highly interpretable. In selecting features, instead of only using correlation, we take causal information into account. Specifically, we adopt the Gaussian processes-based convergent cross mapping framework for causal discovery which is proven to be more reliable than the Granger causality when time series are coupled. Moreover, we introduce a novel method for selecting the history or look-back length of features from the perspective of a dynamical system in a principled manner. The quasi-periodicities that commonly exist in observations of volumes of patients and environment variables can readily be accommodated. Further, the proposed method performs well even in cases when the data are scarce. Also, the approach can be modified without much difficulty to forecast other types of patient volumes. We validate the method with synthetic and real-world datasets.

Transmission trend of the COVID-19 pandemic predicted by dendritic neural regression

In 2020, a novel coronavirus disease became a global problem. The disease was called COVID-19, as the first patient was diagnosed in December 2019. The disease spread around the world quickly due to its powerful viral ability. To date, the spread of COVID-19 has been relatively mild in China due to timely control measures. However, in other countries, the pandemic remains severe, and COVID-19 protection and control policies are urgently needed, which has motivated this research. Since the outbreak of the pandemic, many researchers have hoped to identify the mechanism of COVID-19 transmission and predict its spread by using machine learning (ML) methods to supply meaningful reference information to decision-makers in various countries. Since the historical data of COVID-19 is time series data, most researchers have adopted recurrent neural networks (RNNs), which can capture time information, for this problem. However, even with a state-of-the-art RNN, it is still difficult to perfectly capture the temporal information and nonlinear characteristics from the historical data of COVID-19. Therefore, in this study, we develop a novel dendritic neural regression (DNR) method to improve prediction performance. In the DNR, the multiplication operator is used to capture the nonlinear relationships between input feature signals in the dendrite layer. Considering the complex and large landscape of DNR's weight space, a new scale-free state-of-matter search (SFSMS) algorithm is proposed to optimize the DNR, which combines the state-of-matter search algorithm with a scale-free local search. The SFSMS achieves a better global search ability and thus can effectively reduce the possibility of falling into local minima. In addition, according to Takens's theorem, phase space reconstruction techniques are used to discover the information hidden in the high-dimensional space of COVID-19 data, which further improves the precision of prediction. The experimental results suggest that the proposed method is more competitive in solving this problem than other prevailing methods.

An Autoencoder-Based Deep Learning Approach for Load Identification in Structural Dynamics

In civil engineering, different machine learning algorithms have been adopted to process the huge amount of data continuously acquired through sensor networks and solve inverse problems. Challenging issues linked to structural health monitoring or load identification are currently related to big data, consisting of structural vibration recordings shaped as a multivariate time series. Any algorithm should therefore allow an effective dimensionality reduction, retaining the informative content of data and inferring correlations within and across the time series. Within this framework, we propose a time series AutoEncoder (AE) employing inception modules and residual learning for the encoding and the decoding parts, and an extremely reduced latent representation specifically tailored to tackle load identification tasks. We discuss the choice of the dimensionality of this latent representation, considering the sources of variability in the recordings and the inverse-forward nature of the AE. To help setting the aforementioned dimensionality, the false nearest neighbor heuristics is also exploited. The reported numerical results, related to shear buildings excited by dynamic loadings, highlight the signal reconstruction capacity of the proposed AE, and the capability to accomplish the load identification task.