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

Shrunken Social Brains? A Minimal Model of the Role of Social Interaction in Neural Complexity

The social brain hypothesis proposes that enlarged brains have evolved in response to the increasing cognitive demands that complex social life in larger groups places on primates and other mammals. However, this reasoning can be challenged by evidence that brain size has decreased in the evolutionary transitions from solitary to social larger groups in the case of Neolithic humans and some eusocial insects. Different hypotheses can be identified in the literature to explain this reduction in brain size. We evaluate some of them from the perspective of recent approaches to cognitive science, which support the idea that the basis of cognition can span over brain, body, and environment. Here we show through a minimal cognitive model using an evolutionary robotics methodology that the neural complexity, in terms of neural entropy and degrees of freedom of neural activity, of smaller-brained agents evolved in social interaction is comparable to the neural complexity of larger-brained agents evolved in solitary conditions. The nonlinear time series analysis of agents' neural activity reveals that the decoupled smaller neural network is intrinsically lower dimensional than the decoupled larger neural network. However, when smaller-brained agents are interacting, their actual neural complexity goes beyond its intrinsic limits achieving results comparable to those obtained by larger-brained solitary agents. This suggests that the smaller-brained agents are able to enhance their neural complexity through social interaction, thereby offsetting the reduced brain size.

Analysis of EEG Data Using Complex Geometric Structurization

Electroencephalogram (EEG) is a common tool used to understand brain activities. The data are typically obtained by placing electrodes at the surface of the scalp and recording the oscillations of currents passing through the electrodes. These oscillations can sometimes lead to various interpretations, depending on, for example, the subject's health condition, the experiment carried out, the sensitivity of the tools used, or human manipulations. The data obtained over time can be considered a time series. There is evidence in the literature that epilepsy EEG data may be chaotic. Either way, the Embedding Theory in dynamical systems suggests that time series from a complex system could be used to reconstruct its phase space under proper conditions. In this letter, we propose an analysis of epilepsy EEG time series data based on a novel approach dubbed complex geometric structurization. Complex geometric structurization stems from the construction of strange attractors using Embedding Theory from dynamical systems. The complex geometric structures are themselves obtained using a geometry tool, the α-shapes from shape analysis. Initial analyses show a proof of concept in that these complex structures capture the expected changes brain in lobes under consideration. Further, a deeper analysis suggests that these complex structures can be used as biomarkers for seizure changes.

ordpy: A Python package for data analysis with permutation entropy and ordinal network methods

Since Bandt and Pompe's seminal work, permutation entropy has been used in several applications and is now an essential tool for time series analysis. Beyond becoming a popular and successful technique, permutation entropy inspired a framework for mapping time series into symbolic sequences that triggered the development of many other tools, including an approach for creating networks from time series known as ordinal networks. Despite increasing popularity, the computational development of these methods is fragmented, and there were still no efforts focusing on creating a unified software package. Here, we present ordpy (http://github.com/arthurpessa/ordpy), a simple and open-source Python module that implements permutation entropy and several of the principal methods related to Bandt and Pompe's framework to analyze time series and two-dimensional data. In particular, ordpy implements permutation entropy, Tsallis and Rényi permutation entropies, complexity-entropy plane, complexity-entropy curves, missing ordinal patterns, ordinal networks, and missing ordinal transitions for one-dimensional (time series) and two-dimensional (images) data as well as their multiscale generalizations. We review some theoretical aspects of these tools and illustrate the use of ordpy by replicating several literature results.

Structural classification of proteins based on the computationally efficient recurrence quantification analysis and horizontal visibility graphs

MOTIVATION

Protein structural class prediction is one of the most significant problems in bioinformatics, as it has a prominent role in understanding the function and evolution of proteins. Designing a computationally efficient but at the same time accurate prediction method remains a pressing issue, especially for sequences that we cannot obtain a sufficient amount of homologous information from existing protein sequence databases. Several studies demonstrate the potential of utilizing chaos game representation (CGR) along with time series analysis tools such as recurrence quantification analysis (RQA), complex networks, horizontal visibility graphs (HVG) and others. However, the majority of existing works involve a large amount of features and they require an exhaustive, time consuming search of the optimal parameters. To address the aforementioned problems, this work adopts the generalized multidimensional recurrence quantification analysis (GmdRQA) as an efficient tool that enables to process concurrently a multidimensional time series and reduce the number of features. In addition, two data-driven algorithms, namely average mutual information (AMI) and false nearest neighbors (FNN), are utilized to define in a fast yet precise manner the optimal GmdRQA parameters.

RESULTS

The classification accuracy is improved by the combination of GmdRQA with the HVG. Experimental evaluation on a real benchmark dataset demonstrates that our methods achieve similar performance with the state-of-the-art but with a smaller computational cost.

AVAILABILITY

The code to reproduce all the results is available at https://github.com/aretiz/protein_structure_classification/tree/main.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

An Approach to Aligning Categorical and Continuous Time Series for Studying the Dynamics of Complex Human Behavior

An emerging perspective on human cognition and performance sees it as a kind of self-organizing phenomenon involving dynamic coordination across the body, brain and environment. Measuring this coordination faces a major challenge. Time series obtained from such cognitive, behavioral, and physiological coordination are often complicated in terms of non-stationarity and non-linearity, and in terms of continuous vs. categorical scales. Researchers have proposed several analytical tools and frameworks. One method designed to overcome these complexities is recurrence quantification analysis, developed in the study of non-linear dynamics. It has been applied in various domains, including linguistic (categorical) data or motion (continuous) data. However, most previous studies have applied recurrence methods individually to categorical or continuous data. To understand how complex coordination works, an integration of these types of behavior is needed. We aimed to integrate these methods to investigate the relationship between language (categorical) and motion (continuous) directly. To do so, we added temporal information (a time stamp) to categorical data (i.e., language), and applied joint recurrence analysis methods to visualize and quantify speech-motion coordination coupling during a rap performance. We illustrate how new dynamic methods may capture this coordination in a small case-study design on this expert rap performance. We describe a case study suggesting this kind of dynamic analysis holds promise, and end by discussing the theoretical implications of studying complex performances of this kind as a dynamic, coordinated phenomenon.

Low dimensional manifolds in reservoir computers

A reservoir computer is a complex dynamical system, often created by coupling nonlinear nodes in a network. The nodes are all driven by a common driving signal. Reservoir computers can contain hundreds to thousands of nodes, resulting in a high dimensional dynamical system, but the reservoir computer variables evolve on a lower dimensional manifold in this high dimensional space. This paper describes how this manifold dimension depends on the parameters of the reservoir computer, and how the manifold dimension is related to the performance of the reservoir computer at a signal estimation task. It is demonstrated that increasing the coupling between nodes while controlling the largest Lyapunov exponent of the reservoir computer can optimize the reservoir computer performance. It is also noted that the sparsity of the reservoir computer network does not have any influence on performance.

Towards Embedded Computation with Building Materials

We present results showing the capability of concrete-based information processing substrate in the signal classification task in accordance with in materio computing paradigm. As the Reservoir Computing is a suitable model for describing embedded in materio computation, we propose that this type of presented basic construction unit can be used as a source for “reservoir of states” necessary for simple tuning of the readout layer. We present an electrical characterization of the set of samples with different additive concentrations followed by a dynamical analysis of selected specimens showing fingerprints of memfractive properties. As part of dynamic analysis, several fractal dimensions and entropy parameters for the output signal were analyzed to explore the richness of the reservoir configuration space. In addition, to investigate the chaotic nature and self-affinity of the signal, Lyapunov exponents and Detrended Fluctuation Analysis exponents were calculated. Moreover, on the basis of obtained parameters, classification of the signal waveform shapes can be performed in scenarios explicitly tuned for a given device terminal.

Complexity of Body Movements during Sleep in Children with Autism Spectrum Disorder

Recently, measuring the complexity of body movements during sleep has been proven as an objective biomarker of various psychiatric disorders. Although sleep problems are common in children with autism spectrum disorder (ASD) and might exacerbate ASD symptoms, their objectivity as a biomarker remains to be established. Therefore, details of body movement complexity during sleep as estimated by actigraphy were investigated in typically developing (TD) children and in children with ASD. Several complexity analyses were applied to raw and thresholded data of actigraphy from 17 TD children and 17 children with ASD. Determinism, irregularity and unpredictability, and long-range temporal correlation were examined respectively using the false nearest neighbor (FNN) algorithm, information-theoretic analyses, and detrended fluctuation analysis (DFA). Although the FNN algorithm did not reveal determinism in body movements, surrogate analyses identified the influence of nonlinear processes on the irregularity and long-range temporal correlation of body movements. Additionally, the irregularity and unpredictability of body movements measured by expanded sample entropy were significantly lower in ASD than in TD children up to two hours after sleep onset and at approximately six hours after sleep onset. This difference was found especially for the high-irregularity period. Through this study, we characterized details of the complexity of body movements during sleep and demonstrated the group difference of body movement complexity across TD children and children with ASD. Complexity analyses of body movements during sleep have provided valuable insights into sleep profiles. Body movement complexity might be useful as a biomarker for ASD.

Gazing down increases standing and walking postural steadiness

When walking on an uneven surface or complex terrain, humans tend to gaze downward. This behaviour is usually interpreted as an attempt to acquire useful information to guide locomotion. Visual information, however, is not used exclusively for guiding locomotion; it is also useful for postural control. Both locomotive and postural control have been shown to be sensitive to the visual flow arising from the respective motion of the individual and the three-dimensional environment. This flow changes when a person gazes downward and may present information that is more appropriate for postural control. To investigate whether downward gazing can be used for postural control, rather than exclusively for guiding locomotion, we quantified the dynamics of standing and walking posture in healthy adults, under several visual conditions. Through these experiments we were able to demonstrate that gazing downward, just a few steps ahead, resulted in a steadier standing and walking posture. These experiments indicate that gazing downward may serve more than one purpose and provide sufficient evidence of the possible interplay between the visual information used for guiding locomotion and that used for postural control. These findings contribute to our understanding of the control mechanism/s underlying gait and posture and have possible clinical implications.

Which subject-related variables contribute to movement variability during a simulated repetitive and standardised occupational task? Recurrence quantification analysis of surface electromyographic signals

Movement variability is a component of human movement. This study applied recurrence quantification analysis (RQA) on electromyographic signals to determine the effects of two types of variables on movement variability during a short, simulated repetitive and standardised occupational clip-fitting task. The electrical activity of six muscles in the dominant upper limb was recorded in 21 participants. Variables related to the task performance (insertion force and movements performed when fitting clips) affected RQA measures: recurrence rate (RR), percentage of determinism (DET) and diagonal line length entropy (ENT). Variables related to participant's characteristics (sex, age, and BMI) affected only DET and ENT. A constrasting variability was observed such as a high-DET value combined with a high-ENT value and inversely. Variables affected mainly the recurrences organisation of the more distal muscles. Even if movement variability is complex, it should be considered by ergonomists and work place designers to better understanding of operators' movements. Practitioner summary: It is essential to consider the complexity of operators' movement variability to understand their activities. Based on intrinsic movement variability knowledge, ergonomists and work place designers will be able to modulate the movement variability by acting on workstation designs and occupational organisation with the aim of preserving operators' health. Abbreviations: RR: recurrence rate; DET: percentage of determinism; ENT: diagonal line length entropy; BMI: body mass index; FDS: flexor digitorum superficialis; EXT: extensor digitorum communis; BIC: biceps brachii; TRI: triceps brachii; DEL: deltoideus anterior; TRA: trapezius pars descendens; F: female; M: male; S: supinated; P: pronated; CM: continuous movement; DM: discontinuous movement.

Running barefoot leads to lower running stability compared to shod running - results from a randomized controlled study

Local dynamic running stability is the ability of a dynamic system to compensate for small perturbations during running. While the immediate effects of footwear on running biomechanics are frequently investigated, no research has studied the long-term effects of barefoot vs. shod running on local dynamic running stability. In this randomized single-blinded controlled trial, young adults novice to barefoot running were randomly allocated to a barefoot or a cushioned footwear running group. Over an 8-week-period, both groups performed a weekly 15-min treadmill running intervention in the allocated condition at 70% of their VO2 max velocity. During each session, an inertial measurement unit on the tibia recorded kinematic data (angular velocity) which was used to determine the short-time largest Lyapunov exponents as a measure of local dynamic running stability. One hundred running gait cycles at the beginning, middle, and end of each running session were analysed using one mixed linear multilevel random intercept model. Of the 41 included participants (48.8% females), 37 completed the study (drop-out = 9.7%). Participants in the barefoot running group exhibited lower running stability than in the shod running group (p = 0.037) with no changes during the intervention period (p = 0.997). Within a single session, running stability decreased over the course of the 15-min run (p = 0.012) without differences between both groups (p = 0.060). Changing from shod to barefoot running reduces running stability not only in the acute phase but also in the longer term. While running stability is a relatively new concept, it enables further insight into the biomechanical influence of footwear.

Balance, gait, and navigation performance are related to physical exercise in blind and visually impaired children and adolescents

Self-motion perception used for locomotion and navigation requires the integration of visual, vestibular, and proprioceptive input. In the absence of vision, postural stability and locomotor tasks become more difficult. Previous research has suggested that in visually deprived children, postural stability and levels of physical activity are overall lower than in sighted controls. Here we hypothesized that visually impaired and blind children and adolescents differ from sighted controls in postural stability and gait parameters, and that physically active individuals outperform sedentary peers in postural stability and gait parameters as well as in navigation performance. Fourteen blind and visually impaired children and adolescents (8-18 years of age) and 14 matched sighted individuals took part. Assessments included postural sway, single-leg stance time, parameters of gait variability and stability, self-reported physical activity, and navigation performance. Postural sway was larger and single-leg stance time was lower in blind and visually impaired participants than in blindfolded sighted individuals. Physical activity was higher in the sighted group. No differences between the group of blind and visually impaired and blindfolded sighted participants were observed for gait parameters and navigation performance. Higher levels of physical activity were related to lower postural sway, longer single-leg stance time, higher gait stability, and superior navigation performance in blind and visually impaired participants. The present data suggest that physical activity may enhance postural stability and gait parameters, and thereby promote navigation performance in blind and visually impaired children and adolescents.

A Simple Dendritic Neural Network Model-Based Approach for Daily PM2.5 Concentration Prediction

Air pollution in cities has a massive impact on human health, and an increase in fine particulate matter (PM2.5) concentrations is the main reason for air pollution. Due to the chaotic and intrinsic complexities of PM2.5 concentration time series, it is difficult to utilize traditional approaches to extract useful information from these data. Therefore, a neural model with a dendritic mechanism trained via the states of matter search algorithm (SDNN) is employed to conduct daily PM2.5 concentration forecasting. Primarily, the time delay and embedding dimensions are calculated via the mutual information-based method and false nearest neighbours approach to train the data, respectively. Then, the phase space reconstruction is performed to map the PM2.5 concentration time series into a high-dimensional space based on the obtained time delay and embedding dimensions. Finally, the SDNN is employed to forecast the PM2.5 concentration. The effectiveness of this approach is verified through extensive experimental evaluations, which collect six real-world datasets from recent years. To the best of our knowledge, this study is the first attempt to utilize a dendritic neural model to perform real-world air quality forecasting. The extensive experimental results demonstrate that the SDNN offers very competitive performance relative to the latest prediction techniques.

Trunk Postural Control Strategies Among Persons With Lower-Limb Amputation While Walking and Performing a Concurrent Task

Altered trunk movements during gait in persons with lower-limb amputation are often associated with an increased risk for secondary health conditions; however, the postural control strategies underlying such alterations remain unclear. In this secondary analysis, the authors employed nonlinear measures of triplanar trunk accelerations via short-term Lyapunov exponents to investigate trunk local stability as well as spatiotemporal gait parameters to describe gait mechanics. The authors also evaluated the influence of a concurrent task on trunk local stability and gait mechanics to explore if competition for neuromuscular processing resources can assist in identifying unique strategies to control kinematic variability. Sixteen males with amputation-8 transtibial and 8 transfemoral-and 8 uninjured males (controls) walked on a treadmill at their self-selected speed (mean = 1.2 m/s ±10%) in 5 experimental conditions (8 min each): 4 while performing a concurrent task (2 walking and 2 seated) and 1 with no concurrent task. Individuals with amputation demonstrated significantly smaller Lyapunov exponents than controls in all 3 planes of motion, regardless of concurrent task or level of amputation (P < .0001). Individuals with transfemoral amputation walked with wider strides compared with individuals with transtibial amputation and controls (P < .0001). Individuals with amputation demonstrated more trunk kinematic variability in the presence of wider strides compared with individuals without amputation, and it appears that performing a concurrent cognitive task while walking did not change trunk or gait mechanics.

Multi-Chaotic Analysis of Inter-Beat (R-R) Intervals in Cardiac Signals for Discrimination between Normal and Pathological Classes

Cardiac signals have complex structures representing a combination of simpler structures. In this paper, we develop a new data analytic tool that can extract the complex structures of cardiac signals using the framework of multi-chaotic analysis, which is based on the p-norm for calculating the largest Lyapunov exponent (LLE). Appling the p-norm is useful for deriving the spectrum of the generalized largest Lyapunov exponents (GLLE), which is characterized by the width of the spectrum (which we denote by W). This quantity measures the degree of multi-chaos of the process and can potentially be used to discriminate between different classes of cardiac signals. We propose the joint use of the GLLE and spectrum width to investigate the multi-chaotic behavior of inter-beat (R-R) intervals of cardiac signals recorded from 54 healthy subjects (hs), 44 subjects diagnosed with congestive heart failure (chf), and 25 subjects diagnosed with atrial fibrillation (af). With the proposed approach, we build a regression model for the diagnosis of pathology. Multi-chaotic analysis showed a good performance, allowing the underlying dynamics of the system that generates the heart beat to be examined and expert systems to be built for the diagnosis of cardiac pathologies.

Heat flow random walks in biomolecular systems using symbolic transfer entropy and graph theory

This study combines the information- and graph-theoretic measures to investigate the cluster modulation of the amino acid residues and nucleotides at complex biomolecular interfaces. The symbolic transfer entropy is used as an information-theoretic measure. I also used graph theory to obtain information and heat flow weighted digraph models used to study the topology of information and heat flow paths at complex biomolecular interfaces. I introduce the graph-theoretic measures, such as the influence score and betweenness centrality, to identify the most influential amino acid and nucleotide sequences as sources of the information and absorb centers of the structure's heat flow. PageRank-like random walks algorithm is used to analyze the network of amino acid and nucleotide sequences at the protein-RNA interface combined with weighted digraph models. The cluster analysis using graph-theoretic measures revealed the modular molecular structure and the mechanism of the binding interface. In this study, the first benchmark system is an intuitive directed information flow network used to test the algorithms, and the second benchmark is a protein-RNA complex system. The approach was able to identify the most influential amino acid residues and nucleotides. Furthermore, the statistical cluster analysis using graph-theoretic measures revealed the modular molecular structure and the binding mechanism at the interface.

Sharp decrease in the Laplacian matrix rank of phase-space graphs: a potential biomarker in epilepsy

In this paper, phase space reconstruction from stereo-electroencephalography data of ten patients with focal epilepsy forms a series of graphs. Those obtained graphs reflect the transition characteristics of brain dynamical system from pre-seizure to seizure of epilepsy. Interestingly, it is found that the rank of Laplacian matrix of these graphs has a sharp decrease when a seizure is close to happen, which thus might be viewed as a new potential biomarker in epilepsy. In addition, the reliability of this method is numerically verified with a coupled mass neural model. In particular, our simulation suggests that this potential biomarker can play the roles of predictive effect or delayed awareness, depending on the bias current of the Gaussian noise. These results may give new insights into the seizure detection.

Estimation of Consecutively Missed Samples in Fetal Heart Rate Recordings

During labor, fetal heart rate (FHR) is monitored externally using Doppler ultrasound. This is done continuously, but for various reasons (e.g., fetal or maternal movements) the system does not record any samples for varying periods of time. In many settings, it would be quite beneficial to estimate the missing samples. In this paper, we propose a (deep) Gaussian process-based approach for estimation of consecutively missing samples in FHR recordings. The method relies on similarities in the state space and on exploiting the concept of attractor manifolds. The proposed approach was tested on a short segment of real FHR recordings. The experimental results indicate that the proposed approach is able to provide more reliable results in comparison to several interpolation methods that are commonly applied for processing of FHR signals.

On the use of patterns obtained from LSTM and feature-based methods for time series analysis: application in automatic classification of the CAP A phase subtypes

The cyclic alternating pattern is a marker of sleep instability identified in the electroencephalogram signals whose sequence of transient variations compose the A phases. These phases are divided into three subtypes (A1, A2, and A3) according to the presented patterns. The traditional approach of manually scoring the cyclic alternating pattern events for the full night is unpractical, with a high probability of miss classification, due to the large quantity of information that is produced during a full night recording. To address this concern, automatic methodologies were proposed using a long short-term memory to perform the classification of one electroencephalogram monopolar derivation signal. The proposed model is composed of three classifiers, one for each subtype, performing binary classification in a one versus all procedure. Two methodologies were tested: feed the pre-processed electroencephalogram signal to the classifiers; create features from the pre-processed electroencephalogram signal which were fed to the classifiers (feature-based methods). It was verified that the A1 subtype classification performance was similar for both methods and the A2 subtype classification was higher for the feature-based methods. However, the A3 subtype classification was found to be the most challenging to be performed, and for this classification, the feature-based methods were superior. A characterization analysis was also performed using a recurrence quantification analysis to further examine the subtypes characteristics. The average accuracy and area under the receiver operating characteristic curve for the A1, A2, and A3 subtypes of the feature-based methods were respectively: 82% and 0.92; 80% and 0.88; 85% and 0.86.

Coupled Gluteus Maximus and Gluteus Medius Recruitment Patterns Modulate Hip Adduction Variability During Single-Limb Step-Downs: A Cross-Sectional Study

CONTEXT

Examining the coordinated coupling of muscle recruitment patterns may provide insight into movement variability in sport-related tasks.

OBJECTIVE

The purpose of this study was to examine the relationship between coupled gluteus maximus and medius recruitment patterns and hip-adduction variability during single-limb step-downs.

DESIGN

Cross-sectional.

SETTING

Biomechanics laboratory.

PARTICIPANTS

Forty healthy adults, including 26 women and 14 men, mean age 23.8 (1.6) years, mean body mass index 24.2 (3.1) kg/m2, participated.

INTERVENTIONS

Lower-extremity kinematics were acquired during 20 single-limb step-downs from a 19-cm step height. Electromyography (EMG) signals were captured with surface electrodes. Isometric hip-extension strength was obtained.

MAIN OUTCOME MEASURES

Hip-adduction variability, measured as the SD of peak hip adduction across 20 repetitions of the step-down task, was measured. The mean amplitudes of gluteus maximus and gluteus medius EMG recruitment were examined. Determinism and entropy of the coupled EMG signals were computed with cross-recurrence quantification analyses.

RESULTS

Hip-adduction variability correlated inversely with determinism (r = -.453, P = .018) and positively with entropy (r = .409, P = .034) in coupled gluteus maximus/medius recruitment patterns but not with hip-extensor strength nor with magnitudes of mean gluteus maximus or medius recruitment (r = -.003, .081, and .035; P = .990, .688, and .864, respectively).

CONCLUSION

Hip-adduction variability during single-limb step-downs correlated more strongly with measures of coupled gluteus maximus and medius recruitment patterns than with hip-extensor strength or magnitudes of muscle recruitment. Examining coupled recruitment patterns may provide an alternative understanding of the extent to which hip neuromuscular control modulates lower-extremity kinematics beyond examining muscle strength or EMG recruitment magnitudes.

Fractal analysis of recurrence networks constructed from the two-dimensional fractional Brownian motions

In this study, we focus on the fractal property of recurrence networks constructed from the two-dimensional fractional Brownian motion (2D fBm), i.e., the inter-system recurrence network, the joint recurrence network, the cross-joint recurrence network, and the multidimensional recurrence network, which are the variants of classic recurrence networks extended for multiple time series. Generally, the fractal dimension of these recurrence networks can only be estimated numerically. The numerical analysis identifies the existence of fractality in these constructed recurrence networks. Furthermore, it is found that the numerically estimated fractal dimension of these networks can be connected to the theoretical fractal dimension of the 2D fBm graphs, because both fractal dimensions are piecewisely associated with the Hurst exponent H in a highly similar pattern, i.e., a linear decrease (if H varies from 0 to 0.5) followed by an inversely proportional-like decay (if H changes from 0.5 to 1). Although their fractal dimensions are not exactly identical, their difference can actually be deciphered by one single parameter with the value around 1. Therefore, it can be concluded that these recurrence networks constructed from the 2D fBms must inherit some fractal properties of its associated 2D fBms with respect to the fBm graphs.

Differentiation of pain levels by deploying various EEG synchronization features and dynamic ensemble selection mechanism

OBJECTIVE

The target of this study is measuring the pain intensity in an objective manner by analysing the electroencephalogram (EEG) signals. Although this problem has attracted researchers' attention, increasing the resolution of this measurement, by increasing the number of pain states, significantly decreases the accuracy of pain level classification problem.

APPROACH

To overcome this drawback, we adopt state-of-the-art synchronization schemes to measure the linear, nonlinear and generalized synchronization between different EEG channels. 32 subjects executed the Cold Pressor Task (CPT) and experienced five defined levels of pain while recording their EEGs. Due to high number of synchronization features from 34 channels, the most discriminative features were selected using greedy overall relevancy (GOR) method. The selected features are applied to a dynamic ensemble selection system.

MAIN RESULTS

Our experiment provides 85.6% accuracy over the five classes, which significantly outperforms the results of past research. Moreover, we observe that the selected features belong to the channels placed over the ridge of cortex, the area responsible for processing somatic sensation arisen from nociceptive temperature. As expected, we noted that continuing the painful stimulus for minutes engaged regions beyond the sensorimotor cortex, e.g., the prefrontal cortex.

SIGNIFICANCE

We conclude that the amount of synchronization between scalp EEG channels is an informative tool in revealing the pain sensation.

Multi-level modeling with nonlinear movement metrics to classify self-injurious behaviors in autism spectrum disorder

Self-injurious behavior (SIB) is among the most dangerous concerns in autism spectrum disorder (ASD), often requiring detailed and tedious management methods. Sensor-based behavioral monitoring could address the limitations of these methods, though the complex problem of classifying variable behavior should be addressed first. We aimed to address this need by developing a group-level model accounting for individual variability and potential nonlinear trends in SIB, as a secondary analysis of existing data. Ten participants with ASD and SIB engaged in free play while wearing accelerometers. Movement data were collected from > 200 episodes and 18 different types of SIB. Frequency domain and linear movement variability measures of acceleration signals were extracted to capture differences in behaviors, and metrics of nonlinear movement variability were used to quantify the complexity of SIB. The multi-level logistic regression model, comprising of 12 principal components, explained > 65% of the variance, and classified SIB with > 75% accuracy. Our findings imply that frequency-domain and movement variability metrics can effectively predict SIB. Our modeling approach yielded superior accuracy than commonly used classifiers (~ 75 vs. ~ 64% accuracy) and had superior performance compared to prior reports (~ 75 vs. ~ 69% accuracy) This work provides an approach to generating an accurate and interpretable group-level model for SIB identification, and further supports the feasibility of developing a real-time SIB monitoring system.

Distinguishing Epileptiform Discharges From Normal Electroencephalograms Using Scale-Dependent Lyapunov Exponent

Epileptiform discharges are of fundamental importance in understanding the physiology of epilepsy. To aid in the clinical diagnosis, classification, prognosis, and treatment of epilepsy, it is important to develop automated computer programs to distinguish epileptiform discharges from normal electroencephalogram (EEG). This is a challenging task as clinically used scalp EEG often contains a lot of noise and motion artifacts. The challenge is even greater if one wishes to develop explainable rather than black-box based approaches. To take on this challenge, we propose to use a multiscale complexity measure, the scale-dependent Lyapunov exponent (SDLE). We analyzed 640 multi-channel EEG segments, each 4 s long. Among these segments, 540 are short epileptiform discharges, and 100 are from healthy controls. We found that features from SDLE were very effective in distinguishing epileptiform discharges from normal EEG. Using Random Forest Classifier (RF) and Support Vector Machines (SVM), the proposed approach with different features from SDLE robustly achieves an accuracy exceeding 99% in distinguishing epileptiform discharges from normal control ones. A single parameter, which is the ratio of the spectral energy of EEG signals and the SDLE and quantifies the regularity or predictability of the EEG signals, is introduced to better understand the high accuracy in the classification. It is found that this regularity is considerably greater for epileptiform discharges than for normal controls. Robustly having high accuracy in distinguishing epileptiform discharges from normal controls irrespective of which classification scheme being used, the proposed approach has the potential to be used widely in a clinical setting.

The extended Granger causality analysis for Hodgkin-Huxley neuronal models

How to extract directions of information flow in dynamical systems based on empirical data remains a key challenge. The Granger causality (GC) analysis has been identified as a powerful method to achieve this capability. However, the framework of the GC theory requires that the dynamics of the investigated system can be statistically linearized; i.e., the dynamics can be effectively modeled by linear regressive processes. Under such conditions, the causal connectivity can be directly mapped to the structural connectivity that mediates physical interactions within the system. However, for nonlinear dynamical systems such as the Hodgkin-Huxley (HH) neuronal circuit, the validity of the GC analysis has yet been addressed; namely, whether the constructed causal connectivity is still identical to the synaptic connectivity between neurons remains unknown. In this work, we apply the nonlinear extension of the GC analysis, i.e., the extended GC analysis, to the voltage time series obtained by evolving the HH neuronal network. In addition, we add a certain amount of measurement or observational noise to the time series to take into account the realistic situation in data acquisition in the experiment. Our numerical results indicate that the causal connectivity obtained through the extended GC analysis is consistent with the underlying synaptic connectivity of the system. This consistency is also insensitive to dynamical regimes, e.g., a chaotic or non-chaotic regime. Since the extended GC analysis could in principle be applied to any nonlinear dynamical system as long as its attractor is low dimensional, our results may potentially be extended to the GC analysis in other settings.

Seasonal dynamics of terrestrially sourced nitrogen influenced Karenia brevis blooms off Florida's southern Gulf Coast

Harmful algal blooms (HABs) threaten coastal ecological systems, public health, and local economies, but the complex physical, chemical, and biological processes that culminate in HABs vary by locale and are often poorly understood. Despite broad recognition that cultural eutrophication may exacerbate nearshore bloom events, the association is typically not linear and is often difficult to quantify. Off the Gulf Coast of Florida, Karenia brevis blooms initiate in the open waters of the Gulf of Mexico, and advection of cells supplies nearshore blooms. However, past work has struggled to describe the relationship between terrestrial nutrient runoff and bloom maintenance near the Gulf Coast. This study applied a novel nonlinear time series (NLTS) analytical framework to investigate whether nearshore bloom dynamics observed near Charlotte Harbor, FL were causally and systematically driven by terrestrially sourced inputs of nitrogen, phosphorus, and freshwater between 2012 and 2018. Singular spectrum analysis (SSA) isolated low-dimensional, deterministic signals in K. brevis log₁₀-density dynamics and in the dynamics of nine of 10 candidate drivers. The predominantly seasonal K. brevis signal was strong, explaining 77.6% of the total variance in the observed time series. Causal tests with convergent cross-mapping provided evidence that nitrogen concentrations measured at the discharge point of the Caloosahatchee River systematically influenced K. brevis bloom dynamics. However, further causal testing failed to link these nitrogen dynamics to an upstream basin, possibly due to data limitations. The results support the hypothesis that anthropogenic nitrogen runoff facilitated the growth of K. brevis blooms near Charlotte Harbor and suggest that bloom events would be mitigated by nitrogen source and transport controls within the Caloosahatchee and/or Kissimmee River basins. More broadly, this work demonstrates that management-relevant causal inferences into the drivers of HABs may be drawn from available monitoring records.

A head-worn display ("smart glasses") has adverse impacts on the dynamics of lateral position control during gait

BACKGROUND

Head-worn displays (e.g., "smart glasses") are an emerging technology to provide information, and in many situations they might be used while walking. However, little evidence exists regarding the effects of head-worn displays on walking performance. We found earlier that "smart glasses" had smaller adverse effects on measures of gait variability in the anterior-posterior direction vs. other types of information displays. Participants, however, complained about motion sickness and perceived instability while using smart glasses.

RESEARCH QUESTION

Were the participants' complaints a result of adverse effects of the smart glasses on the dynamics of lateral stepping and gait stability?

METHODS

Twenty individuals walked on a treadmill in four different conditions; single-task walking, and three dual-task walking conditions, the latter using smart glasses, smartphone, and a paper-based system to provide secondary cognitive tasks. We assessed the dynamics of lateral stepping and gait stability using the goal equivalent manifold and maximum Lyapunov exponent, respectively.

RESULTS

The dynamics of the lateral stepping were more adversely affected using smart glasses compared to the other types of information displays. However, stability measures revealed that the participants were more unstable when they used the smartphone and paper-based system.

SIGNIFICANCE

Promising results in terms of stability and adaptability suggest that head-worn display technology is a potentially useful alternative to smartphones and other types of information displays for reducing the risk of a fall. Results regarding perceptions of instability and a loss of control over lateral stepping, however, imply that this technology requires further development prior to real-work implementations.

Intrinsic recurrence quantification analysis of nonlinear and nonstationary short-term time series

Recurrence analysis is a powerful tool to appraise the nonlinear dynamics of complex systems and delineate the inherent laminar, divergent, or transient behaviors. Oftentimes, the effectiveness of recurrence quantification hinges upon the accurate reconstruction of the state space from a univariate time series with a uniform sampling rate. Few, if any, existing approaches quantify the recurrence properties from a short-term time series, particularly those sampled at a non-uniform rate, which are fairly ubiquitous in studies of rare or extreme events. This paper presents a novel intrinsic recurrence quantification analysis to portray the recurrence behaviors in complex dynamical systems with only short-term observations. As opposed to the traditional recurrence analysis, the proposed approach represents recurrence dynamics of a short-term time series in an intrinsic state space formed by proper rotations, attained from intrinsic time-scale decomposition (ITD) of the short time series. It is shown that intrinsic recurrence quantification analysis (iRQA), patterns harnessed from the corresponding recurrence plot, captures the underlying nonlinear and nonstationary dynamics of those short time series. In addition, as ITD does not require uniform sampling of the time series, iRQA is also applicable to unevenly spaced temporal data. Our findings are corroborated in two case studies: change detection in the Lorenz time series and early-stage identification of atrial fibrillation using short-term electrocardiogram signals.

Mediolateral damping of an overhead body weight support system assists stability during treadmill walking

BACKGROUND

Body weight support systems with three or more degrees of freedom (3-DoF) are permissive and safe environments that provide unloading and allow unrestricted movement in any direction. This enables training of walking and balance control at an early stage in rehabilitation. Transparent systems generate a support force vector that is near vertical at all positions in the workspace to only minimally interfere with natural movement patterns. Patients with impaired balance, however, may benefit from additional mediolateral support that can be adjusted according to their capacity. An elegant solution for providing balance support might be by rendering viscous damping along the mediolateral axis via the software controller. Before use with patients, we evaluated if control-rendered mediolateral damping evokes the desired stability enhancement in able-bodied individuals.

METHODS

A transparent, cable-driven robotic body weight support system (FLOAT) was used to provide transparent body weight support with and without mediolateral damping to 21 able-bodied volunteers while walking at preferred gait velocity on a treadmill. Stability metrics reflecting resistance to small and large perturbations were derived from walking kinematics and compared between conditions and to free walking.

RESULTS

Compared to free walking, the application of body weight support per-se resulted in gait alterations typically associated with body weight support, namely increased step length and swing phase. Frontal plane dynamic stability, measured by kinematic variability and nonlinear dynamics of the center of mass, was increased under body weight support, indicating reduced balance requirements in both damped and undamped support conditions. Adding damping to the body weight support resulted in a greater increase of frontal plane stability.

CONCLUSION

Adding mediolateral damping to 3-DoF body weight support systems is an effective method of increasing frontal plane stability during walking in able-bodied participants. Building on these results, adjustable mediolateral damping could enable therapists to select combinations of unloading and stability specifically for each patient and to adapt this in a task specific manner. This could extend the impact of transparent 3-DoF body weight support systems, enabling training of gait and active balance from an early time point onwards in the rehabilitation process for a wide range of mobility activities of daily life.

A Refinement of Recurrence Analysis to Determine the Time Delay of Causality in Presence of External Perturbations

This article describes a refinement of recurrence analysis to determine the delay in the causal influence between a driver and a target, in the presence of additional perturbations affecting the time series of the response observable. The methodology is based on the definition of a new type of recurrence plots, the Conditional Joint Recurrence plot. The potential of the proposed approach resides in the great flexibility of recurrence plots themselves, which allows extending the technique to more than three quantities. Autoregressive time series, both linear and nonlinear, with different couplings and percentage of additive Gaussian noise have been investigated in detail, with and without outliers. The approach has also been applied to the case of synthetic periodic signals, representing realistic situations of synchronization experiments in thermonuclear fusion. The results obtained have been very positive; the proposed Conditional Joint Recurrence plots have always managed to identify the right interval of the causal influences and are very competitive with alternative techniques such as the Conditional Transfer Entropy.

Youth With Concussion Have Less Adaptable Gait Patterns Than Their Uninjured Peers: Implications for Concussion Management

OBJECTIVE

To compare cross-recurrence quantification analysis measurements obtained during gait between adolescents who sustained a diagnosed concussion within 14 days of assessment and healthy adolescents.

DESIGN

Cross-sectional study.

METHODS

Youth athletes with concussion (n = 43; mean ± SD age, 14.4 ± 2.3 years; 56% female; tested median, 7 days post concussion) and healthy controls (n = 38; age, 14.9 ± 2.0 years; 55% female) completed a single-task and dual-task gait protocol while wearing a set of inertial sensors. We used cross-recurrence quantification analysis techniques to quantify the similarity between accelerations obtained from the sensor on the dorsum of each foot. Four outcome variables were compared between groups: percent determinism, average diagonal-line length, laminarity, and trapping time.

RESULTS

Athletes with concussion had significantly higher percent determinism, laminarity, and trapping time than the control group in single-task and dual-task conditions (P<.05). Gait patterns, when simultaneously completing a secondary cognitive task (dual task), were no different from gait patterns under a single-task condition.

CONCLUSION

Higher percent determinism, laminarity, and trapping time among athletes with concussion suggest that concussion may be associated with a more stuck and predictable gait pattern. These altered movement patterns may be one reason for underlying slower gait speeds that have been observed following concussion. J Orthop Sports Phys Ther 2020;50(8):438-446. Epub 22 May 2020. doi:10.2519/jospt.2020.9133.

Chaotic markers in dynamic diffraction

In a dynamic far-field diffraction experiment, we calculate the largest Lyapunov exponent of a time series obtained from the optical fluctuations in a dynamic diffraction pattern. The time series is used to characterize the locomotory predictability of an oversampled microscopic species. We use a live nematode, Caenorhabditis elegans, as a model organism to demonstrate our method. The time series is derived from the intensity at one point in the diffraction pattern. This single time series displays chaotic markers in the locomotion of the Caenorhabditis elegans by reconstructing the multidimensional phase space. The average largest Lyapunov exponent (base e) associated with the dynamic diffraction of 10 adult wildtype (N2) Caenorhabditis elegans is 1.27±0.03s^-1.

Path length statistics in reservoir computers

Because reservoir computers are high dimensional dynamical systems, designing a good reservoir computer is difficult. In many cases, the designer must search a large nonlinear parameter space, and each step of the search requires simulating the full reservoir computer. In this work, I show that a simple statistic based on the mean path length between nodes in the reservoir computer is correlated with better reservoir computer performance. The statistic predicts the diversity of signals produced by the reservoir computer, as measured by the covariance matrix of the reservoir computer. This statistic by itself is not sufficient to predict reservoir computer performance because not only must the reservoir computer produce a diverse set of signals, it must be well matched to the training signals. Nevertheless, this path length statistic allows the designer to eliminate some network configurations from consideration without having to actually simulate the reservoir computer, reducing the complexity of the design process.

Recognition of the idle state based on a novel IFB-OCN method for an asynchronous brain-computer interface

BACKGROUND

A major difficulty for the asynchronous brain-computer interface (BCI) lies in the accurate recognition of the control and idle states. Although subject's attention level was found to be different in these states, the validity of recognizing them using attention features has not been studied.

NEW METHODS

This paper proposed a novel Individualized Frequency Band based Optimized Complex Network (IFB-OCN) method to enhance the performance of discriminating the control and idle states. The IFB-OCN method extracted the attention features from a single FPz channel, selected the first three individualized frequency bands with the highest accuracies, and integrated the features of these bands for classification.

RESULTS

The performance was evaluated using a steady-state visual evoked potential (SSVEP)-based BCI task. In the offline evaluation, the IFB-OCN method achieved the highest average accuracy of 93.5 % with the data length of 4 s, and achieved the highest information transfer rate (ITR) of 47.3 bits/min with the data length of 0.5 s. In the simulated online evaluation, the IFB-OCN method obtained a true positive rate (TPR) of 89.8 % and a true negative rate (TNR) of 86.2 %.

COMPARISON WITH EXISTING METHODS

The proposed IFB-OCN method recognized the control and idle states using a single FPz channel rather than the occipital channels, and outperformed the existing algorithms in the accuracy of detecting the attention level.

CONCLUSIONS

These results demonstrate that the proposed IFB-OCN method is efficient in recognizing the idle state and has a great potential for enhancing the asynchronous BCIs.

New assistive walker improved local dynamic stability in young healthy adults

In this study, we investigated the effect of walker type on gait pattern characteristics comparing normal gait (NG), gait with a regular walker (RW), and gait with a newly developed walker with vertical moveable handlebars, the Crosswalker (CW). Partial weight bearing (PWB) of the feet, peak joint angles and largest Lyapunov exponent (λ_max) of the lower extremities (hip, knee, ankle) in the sagittal plane, and gait parameters (gait velocity, stride length, cadence, stride duration) were determined for 18 healthy young adults performing 10 walking trials for each walking condition. Assistive gait with the CW improved local dynamic stability in the lower extremities (hip, knee, ankle) compared with RW and was not significantly different from NG. However, peak joint angles and stride characteristics in CW were different from NG. The PWB on the feet was lower with the RW (70.3%) compared to NG (82.8%) and CW (80.9%). This improved stability may be beneficial for the elderly and patients with impaired gait. However, increased PWB is not beneficial for patients during the early stages of rehabilitation.

On the structure of time-delay embedding in linear models of non-linear dynamical systems

This work addresses fundamental issues related to the structure and conditioning of linear time-delayed models of non-linear dynamics on an attractor. While this approach has been well-studied in the asymptotic sense (e.g., for an infinite number of delays), the non-asymptotic setting is not well-understood. First, we show that the minimal time-delays required for perfect signal recovery are solely determined by the sparsity in the Fourier spectrum for scalar systems. For the vector case, we provide a rank test and a geometric interpretation for the necessary and sufficient conditions for the existence of an accurate linear time delayed model. Furthermore, we prove that the output controllability index of a linear system induced by the Fourier spectrum serves as a tight upper bound on the minimal number of time delays required. An explicit expression for the exact linear model in the spectral domain is also provided. From a numerical perspective, the effect of the sampling rate and the number of time delays on numerical conditioning is examined. An upper bound on the condition number is derived, with the implication that conditioning can be improved with additional time delays and/or decreasing sampling rates. Moreover, it is explicitly shown that the underlying dynamics can be accurately recovered using only a partial period of the attractor. Our analysis is first validated in simple periodic and quasiperiodic systems, and sensitivity to noise is also investigated. Finally, issues and practical strategies of choosing time delays in large-scale chaotic systems are discussed and demonstrated on 3D turbulent Rayleigh-Bénard convection.

Effect of data length on time delay and embedding dimension for calculating the Lyapunov exponent in walking

The Lyapunov exponent (LyE) is a trending measure for characterizing gait stability. Previous studies have shown that data length has an effect on the resultant LyE, but the origin of why it changes is unknown. This study investigates if data length affects the choice of time delay and embedding dimension when reconstructing the phase space, which is a requirement for calculating the LyE. The effect of three different preprocessing methods on reconstructing the gait attractor was also investigated. Lumbar accelerometer data were collected from 10 healthy subjects walking on a treadmill at their preferred walking speed for 30 min. Our results show that time delay was not sensitive to the amount of data used during calculation. However, the embedding dimension had a minimum data requirement of 200 or 300 gait cycles, depending on the preprocessing method used, to determine the steady-state value of the embedding dimension. This study also found that preprocessing the data using a fixed number of strides or a fixed number of data points had significantly different values for time delay compared to a time series that used a fixed number of normalized gait cycles, which have a fixed number of data points per stride. Thus, comparing LyE values should match the method of calculation using either a fixed number of strides or a fixed number of data points.

Reliability of recurrence quantification analysis of postural sway data. A comparison of two methods to determine recurrence thresholds

Ageing affects balance control resulting in a greater amplitude of sway and alterations in structure of the sway time series. Recurrence quantification analysis (RQA) has been used to determine the structure of center-of-pressure (CoP; a measure that reflects standing postural control) data as a means to quantify how CoP repeats itself / recurs below a certain threshold. This study aimed to determine how the method of threshold determination, below which a recurrence is defined, affects the within-session reliability of RQA in an elderly population. Within-session reliability of RQA of CoP motion in the anterior-posterior and mediolateral directions was assessed in 267 individuals (>65 years old) when standing on firm or foam surface with eyes open or closed for each of two recurrence threshold methods. One threshold method sets the recurrence threshold level such that the recurrence rate is fixed to 5%, the other method sets the recurrence threshold based on 27% of the mean distance between all points from which recurrences are quantified. Reliability across four 30-s balance trials within each of four balance conditions (firm vs. foam, eyes open vs. closed) was determined using intra-class correlation, standard error of measurement and minimal detectable change. ICCs were better, the standard error of measurement and minimal detectable change were smaller when the recurrence threshold was set to 5% using the fixed recurrence threshold. Fixing recurrence rate improves the within session reliability of RQA and could increase sensitivity to identify fall risk.

Effects of triceps surae fatigue and weight training level on gait variability and local stability in young adults

Muscle fatigue negatively affects gait, and the changes in gait pattern due to muscle fatigue is influenced by which muscles are fatigued and pre-existing physical activity levels. However, how these factors alter gait stability and variability, measures related to risk of fall, remains unclear. To explore how muscular fatigue affects linear and nonlinear gait features in young adults, the effects of triceps surae fatigue and weight training level on gait variability and local stability, as well as a 12-min recovery time of post-fatigue period, were evaluated in young adults (trained and untrained groups). Some features were estimated, i.e., (i) step length (SL) and step frequency (SF), (ii) average standard deviation of trunk acceleration along strides (VAR), and (iii) local dynamic stability (LDS; maximum Lyapunov exponent). LDS presented a significant increase in the anterior-posterior direction with recovery to trained group. SL and SF changed immediately post-fatigue and recovered for both groups, while VAR increased significantly in all directions, with a recovery in the vertical direction for both groups and in the medial-lateral direction for trained group. Localized fatigue affected the analyzed gait variables independent of the participant's training condition, and an interval of 12 min does not seem to be enough for a complete recovery, suggesting a longer recovery period after tasks involving localized triceps surae fatigue to guarantee basal levels of gait variability and local stability. Graphical abstract Flow chart of the experimental protocol. A) Pre-fatigue: 4 min walking at PWS. B) Post-fatigue: first 4 min walking after fatigue protocol. C) Post-fatigue: second 4 min walking after fatigue protocol. D) Post-fatigue: third 4 min walking after fatigue protocol (PWS, preferred walking speed; AP, anterior-posterior; V, vertical; ML, medial-lateral).