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

The effect of different ranges of motion on local dynamic stability of the elbow during unloaded repetitive flexion-extension movements

Local dynamic stability (LDS) of movement is controlled primarily by active muscles, and is known to be influenced by factors such as movement speed and inertial load. Other factors such as muscle length, the length of the target trajectory, and the resistance of passive tissues through ranges of motion (ROM) may also influence LDS. This study was designed to examine the effect of ROM, which impacts each of the aforementioned factors, on LDS of the elbow. 16 participants performed 30 unloaded, repetitive, flexion-extension movements of the elbow with varying (1) angular displacement magnitudes: 40° and 80°; (2) locations of ROM: mid-range, flexion end-range, extension end-range; and (3) rotated positions of the forearm: pronated and supinated. LDS was calculated using a finite time Lyapunov analysis of angular elbow flexion-extension kinematic data. EMG-based muscle activation and co-contraction data were also examined for possible mechanisms of stabilization. Results showed no changes in LDS with any movement condition; however, there were significant effects on muscle activation with ROM location and forearm rotated position. This suggests that a consistent level of LDS of the elbow through varying ROMs is maintained, at least in part, by the active control of the elbow flexor and extensor muscles.

A Time Series Approach to Random Number Generation: Using Recurrence Quantification Analysis to Capture Executive Behavior

The concept of executive functions plays a prominent role in contemporary experimental and clinical studies on cognition. One paradigm used in this framework is the random number generation (RNG) task, the execution of which demands aspects of executive functioning, specifically inhibition and working memory. Data from the RNG task are best seen as a series of successive events. However, traditional RNG measures that are used to quantify executive functioning are mostly summary statistics referring to deviations from mathematical randomness. In the current study, we explore the utility of recurrence quantification analysis (RQA), a non-linear method that keeps the entire sequence intact, as a better way to describe executive functioning compared to traditional measures. To this aim, 242 first- and second-year students completed a non-paced RNG task. Principal component analysis of their data showed that traditional and RQA measures convey more or less the same information. However, RQA measures do so more parsimoniously and have a better interpretation.

Harmony from chaos? Perceptual-motor delays enhance behavioral anticipation in social interaction

Effective interpersonal coordination is fundamental to robust social interaction, and the ability to anticipate a coactor's behavior is essential for achieving this coordination. However, coordination research has focused on the behavioral synchrony that occurs between the simple periodic movements of coactors and, thus, little is known about the anticipation that occurs during complex, everyday interaction. Research on the dynamics of coupled neurons, human motor control, electrical circuits, and laser semiconductors universally demonstrates that small temporal feedback delays are necessary for the anticipation of chaotic events. We therefore investigated whether similar feedback delays would promote anticipatory behavior during social interaction. Results revealed that coactors were not only able to anticipate others' chaotic movements when experiencing small perceptual-motor delays, but also exhibited movement patterns of equivalent complexity. This suggests that such delays, including those within the human nervous system, may enhance, rather than hinder, the anticipatory processes that underlie successful social interaction.

Weighted protein residue networks based on joint recurrences between residues

BACKGROUND

Weighted and un-weighted protein residue networks can predict key functional residues in proteins based on the closeness centrality C and betweenness centrality B values for each residue. A static snapshot of the protein structure, and a cutoff distance, are used to define edges between the network nodes. In this work we apply the weighted network approach to study the β-Lactamase Inhibitory Protein (BLIP). Joint recurrences extracted from molecular dynamics MD trajectory positions of the protein residue carbon alpha atoms are used to define edge weights between nodes, and no cutoff distance is used. The results for B and C from our approach are compared with those extracted from an un-weighted network, and a weighted network that uses interatomic contacts to define edge weights between nodes, respectively.

RESULTS

The joint recurrence weighted network approach performs well in pointing out key protein residues. Furthermore, it seems to emphasize residues with medium to high relative solvent accessibility that lie in loop regions between secondary structure elements of the protein.

CONCLUSIONS

Protein residue networks that use joint recurrences extracted from molecular dynamics simulations of a solvated protein perform well in pointing to hotspot residues and hotspot clusters. This approach uses no distance cutoff threshold, and does not exclude any interactions between the residues, including water-mediated interactions.

Forecasting nonlinear chaotic time series with function expression method based on an improved genetic-simulated annealing algorithm

The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior.

Disrupting morphosyntactic and lexical semantic processing has opposite effects on the sample entropy of neural signals

Converging evidence in neuroscience suggests that syntax and semantics are dissociable in brain space and time. However, it is possible that partly disjoint cortical networks, operating in successive time frames, still perform similar types of neural computations. To test the alternative hypothesis, we collected EEG data while participants read sentences containing lexical semantic or morphosyntactic anomalies, resulting in N400 and P600 effects, respectively. Next, we reconstructed phase space trajectories from EEG time series, and we measured the complexity of the resulting dynamical orbits using sample entropy - an index of the rate at which the system generates or loses information over time. Disrupting morphosyntactic or lexical semantic processing had opposite effects on sample entropy: it increased in the N400 window for semantic anomalies, and it decreased in the P600 window for morphosyntactic anomalies. These findings point to a fundamental divergence in the neural computations supporting meaning and grammar in language.

EEMD independent extraction for mixing features of rotating machinery reconstructed in phase space

Empirical Mode Decomposition (EMD), due to its adaptive decomposition property for the non-linear and non-stationary signals, has been widely used in vibration analyses for rotating machinery. However, EMD suffers from mode mixing, which is difficult to extract features independently. Although the improved EMD, well known as the ensemble EMD (EEMD), has been proposed, mode mixing is alleviated only to a certain degree. Moreover, EEMD needs to determine the amplitude of added noise. In this paper, we propose Phase Space Ensemble Empirical Mode Decomposition (PSEEMD) integrating Phase Space Reconstruction (PSR) and Manifold Learning (ML) for modifying EEMD. We also provide the principle and detailed procedure of PSEEMD, and the analyses on a simulation signal and an actual vibration signal derived from a rubbing rotor are performed. The results show that PSEEMD is more efficient and convenient than EEMD in extracting the mixing features from the investigated signal and in optimizing the amplitude of the necessary added noise. Additionally PSEEMD can extract the weak features interfered with a certain amount of noise.

Functional Connectivity in Frequency-Tagged Cortical Networks During Active Harm Avoidance

Many behavioral and cognitive processes are grounded in widespread and dynamic communication between brain regions. Thus, the quantification of functional connectivity with high temporal resolution is highly desirable for capturing in vivo brain function. However, many of the commonly used measures of functional connectivity capture only linear signal dependence and are based entirely on relatively simple quantitative measures such as mean and variance. In this study, the authors used a recently developed algorithm, the generalized measure of association (GMA), to quantify dynamic changes in cortical connectivity using steady-state visual evoked potentials (ssVEPs) measured in the context of a conditioned behavioral avoidance task. GMA uses a nonparametric estimator of statistical dependence based on ranks that are efficient and capable of providing temporal precision roughly corresponding to the timing of cognitive acts (∼ 100-200 msec). Participants viewed simple gratings predicting the presence/absence of an aversive loud noise, co-occurring with peripheral cues indicating whether the loud noise could be avoided by means of a key press (active) or not (passive). For active compared with passive trials, heightened connectivity between visual and central areas was observed in time segments preceding and surrounding the avoidance cue. Viewing of the threat stimuli also led to greater initial connectivity between occipital and central regions, followed by heightened local coupling among visual regions surrounding the motor response. Local neural coupling within extended visual regions was sustained throughout major parts of the viewing epoch. These findings are discussed in a framework of flexible synchronization between cortical networks as a function of experience and active sensorimotor coupling.

Transcranial Magnetic Stimulation Combined with EEG Reveals Covert States of Elevated Excitability in the Human Epileptic Brain

BACKGROUND

Transcranial magnetic stimulation combined with electroencephalogram (TMS-EEG) can be used to explore the dynamical state of neuronal networks. In patients with epilepsy, TMS can induce epileptiform discharges (EDs) with a stochastic occurrence despite constant stimulation parameters. This observation raises the possibility that the pre-stimulation period contains multiple covert states of brain excitability some of which are associated with the generation of EDs.

OBJECTIVE

To investigate whether the interictal period contains "high excitability" states that upon brain stimulation produce EDs and can be differentiated from "low excitability" states producing normal appearing TMS-EEG responses.

METHODS

In a cohort of 25 patients with Genetic Generalized Epilepsies (GGE) we identified two subjects characterized by the intermittent development of TMS-induced EDs. The high-excitability in the pre-stimulation period was assessed using multiple measures of univariate time series analysis. Measures providing optimal discrimination were identified by feature selection techniques. The "high excitability" states emerged in multiple loci (indicating diffuse cortical hyperexcitability) and were clearly differentiated on the basis of 14 measures from "low excitability" states (accuracy = 0.7).

CONCLUSION

In GGE, the interictal period contains multiple, quasi-stable covert states of excitability a class of which is associated with the generation of TMS-induced EDs. The relevance of these findings to theoretical models of ictogenesis is discussed.

n-Order and maximum fuzzy similarity entropy for discrimination of signals of different complexity: Application to fetal heart rate signals

This paper presents two new concepts for discrimination of signals of different complexity. The first focused initially on solving the problem of setting entropy descriptors by varying the pattern size instead of the tolerance. This led to the search for the optimal pattern size that maximized the similarity entropy. The second paradigm was based on the n-order similarity entropy that encompasses the 1-order similarity entropy. To improve the statistical stability, n-order fuzzy similarity entropy was proposed. Fractional Brownian motion was simulated to validate the different methods proposed, and fetal heart rate signals were used to discriminate normal from abnormal fetuses. In all cases, it was found that it was possible to discriminate time series of different complexity such as fractional Brownian motion and fetal heart rate signals. The best levels of performance in terms of sensitivity (90%) and specificity (90%) were obtained with the n-order fuzzy similarity entropy. However, it was shown that the optimal pattern size and the maximum similarity measurement were related to intrinsic features of the time series.

Use of False Nearest Neighbours for Selecting Variables and Embedding Parameters for State Space Reconstruction

If data are generated by a system with a d-dimensional attractor, then Takens’ theorem guarantees that reconstruction that is diffeomorphic to the original attractor can be built from the single time series in 2d+1-dimensional phase space. However, under certain conditions, reconstruction is possible even in a space of smaller dimension. This topic is very important because the size of the reconstruction space relates to the effectiveness of the whole subsequent analysis. In this paper, the false nearest neighbour (FNN) methods are revisited to estimate the optimum embedding parameters and the most appropriate observables for state space reconstruction. A modification of the false nearest neighbour method is introduced. The findings contribute to evidence that the length of the embedding time window (TW) is more important than the reconstruction delay time and the embedding dimension (ED) separately. Moreover, if several time series of the same system are observed, the choice of the one that is used for the reconstruction could also be critical. The results are demonstrated on two chaotic benchmark systems.

Synchronization, non-linear dynamics and low-frequency fluctuations: analogy between spontaneous brain activity and networked single-transistor chaotic oscillators

In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D2), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes.

Understanding dynamic stability from pelvis accelerometer data and the relationship to balance and mobility in transtibial amputees

This study investigated whether pelvis acceleration-derived parameters can differentiate between dynamic stability states for transtibial amputees during level (LG) and uneven ground (UG) walking. Correlations between these parameters and clinical balance and mobility measures were also investigated. A convenience sample of eleven individuals with unilateral transtibial amputation walked on LG and simulated UG while pelvis acceleration data were collected at 100Hz. Descriptive statistics, Fast Fourier Transform, ratio of even to odd harmonics, and maximum Lyapunov exponent measures were derived from acceleration data. Of the 26 pelvis acceleration measures, seven had a significant difference (p≤0.05) between LG and UG walking conditions. Seven distinct, stability-relevant measures appeared in at least one of the six regression models that correlated accelerometer-derived measures to Berg Balance Scale (BBS), Community Balance and Mobility Scale (CBMS), and Prosthesis Evaluation Questionnaire (PEQ) scores, explaining up to 100% of the variability in these measures. Of these seven measures, medial-lateral acceleration range was the most frequent model variable, appearing in four models. Anterior-posterior acceleration standard deviation and stride time appeared in three models. Pelvis acceleration-derived parameters were able to differentiate between LG and UG walking for transtibial amputees. UG walking provided the most relevant data for balance and mobility assessment. These results could translate to point of patient contact assessments using a wearable system such as a smartbelt or accelerometer-equipped smartphone.

Advanced age brings a greater reliance on visual feedback to maintain balance during walking

We implemented a virtual reality system to quantify differences in the use of visual feedback to maintain balance during walking between healthy young (n=12, mean age: 24 years) and healthy old (n=11, 71 years) adults. Subjects walked on a treadmill while watching a speed-matched, virtual hallway with and without mediolateral visual perturbations. A motion capture system tracked center of mass (CoM) motion and foot kinematics. Spectral analysis, detrended fluctuation analysis, and local divergence exponents quantified old and young adults' dynamic response to visual perturbations. Old and young adults walked normally with comparable CoM spectral characteristics, lateral step placement temporal persistence, and local divergence exponents. Perturbed visual flow induced significantly larger changes in mediolateral CoM motion in old vs. young adults. Moreover, visual perturbations disrupted the control of lateral step placement and compromised local dynamic stability more significantly in old than young adults. Advanced age induces a greater reliance on visual feedback to maintain balance during waking, an effect that may compensate for degradations in somatosensation. Our findings are relevant to the early diagnosis of sensory-induced balance impairments and also point to the potential use of virtual reality to evaluate sensory rehabilitation and balance training programs for old adults.

Ordinal symbolic analysis and its application to biomedical recordings

Ordinal symbolic analysis opens an interesting and powerful perspective on time-series analysis. Here, we review this relatively new approach and highlight its relation to symbolic dynamics and representations. Our exposition reaches from the general ideas up to recent developments, with special emphasis on its applications to biomedical recordings. The latter will be illustrated with epilepsy data.

Analyzing long-term correlated stochastic processes by means of recurrence networks: potentials and pitfalls

Long-range correlated processes are ubiquitous, ranging from climate variables to financial time series. One paradigmatic example for such processes is fractional Brownian motion (fBm). In this work, we highlight the potentials and conceptual as well as practical limitations when applying the recently proposed recurrence network (RN) approach to fBm and related stochastic processes. In particular, we demonstrate that the results of a previous application of RN analysis to fBm [Liu et al. Phys. Rev. E 89, 032814 (2014)] are mainly due to an inappropriate treatment disregarding the intrinsic nonstationarity of such processes. Complementarily, we analyze some RN properties of the closely related stationary fractional Gaussian noise (fGn) processes and find that the resulting network properties are well-defined and behave as one would expect from basic conceptual considerations. Our results demonstrate that RN analysis can indeed provide meaningful results for stationary stochastic processes, given a proper selection of its intrinsic methodological parameters, whereas it is prone to fail to uniquely retrieve RN properties for nonstationary stochastic processes like fBm.

Surface EMG parameters in schizophrenia patients

The aim of the study was to compare a variety of surface EMG (sEMG) parameters in several groups of schizophrenia (SZ, n=69) patients and healthy controls (n=44). We computed spectral, mutual information (MI) based and recurrence quantification analysis (RQA) parameters of sEMG. The major finding is that sEMG of the controls had higher values of the MI-based parameter, mean and median spectrum frequencies, and lower values of most of RQA parameters. It means higher content of recurrent fragments in sEMG of SZ patients. We suggest that the differences might be caused by either denervation/renervation process of single muscle fibers in SZ patients and/or by increased motor unit synchronization induced by antipsychotic therapy.

Identification and quantification analysis of nonlinear dynamics properties of combustion instability in a diesel engine

The cycling combustion instabilities in a diesel engine have been analyzed based on chaos theory. The objective was to investigate the dynamical characteristics of combustion in diesel engine. In this study, experiments were performed under the entire operating range of a diesel engine (the engine speed was changed from 600 to 1400 rpm and the engine load rate was from 0% to 100%), and acquired real-time series of in-cylinder combustion pressure using a piezoelectric transducer installed on the cylinder head. Several methods were applied to identify and quantitatively analyze the combustion process complexity in the diesel engine including delay-coordinate embedding, recurrence plot (RP), Recurrence Quantification Analysis, correlation dimension (CD), and the largest Lyapunov exponent (LLE) estimation. The results show that the combustion process exhibits some determinism. If LLE is positive, then the combustion system has a fractal dimension and CD is no more than 1.6 and within the diesel engine operating range. We have concluded that the combustion system of diesel engine is a low-dimensional chaotic system and the maximum values of CD and LLE occur at the lowest engine speed and load. This means that combustion system is more complex and sensitive to initial conditions and that poor combustion quality leads to the decrease of fuel economy and the increase of exhaust emissions.

Analysis and prediction of aperiodic hydrodynamic oscillatory time series by feed-forward neural networks, fuzzy logic, and a local nonlinear predictor

Forecasting of aperiodic time series is a compelling challenge for science. In this work, we analyze aperiodic spectrophotometric data, proportional to the concentrations of two forms of a thermoreversible photochromic spiro-oxazine, that are generated when a cuvette containing a solution of the spiro-oxazine undergoes photoreaction and convection due to localized ultraviolet illumination. We construct the phase space for the system using Takens' theorem and we calculate the Lyapunov exponents and the correlation dimensions to ascertain the chaotic character of the time series. Finally, we predict the time series using three distinct methods: a feed-forward neural network, fuzzy logic, and a local nonlinear predictor. We compare the performances of these three methods.

Detecting causality from nonlinear dynamics with short-term time series

Quantifying causality between variables from observed time series data is of great importance in various disciplines but also a challenging task, especially when the observed data are short. Unlike the conventional methods, we find it possible to detect causality only with very short time series data, based on embedding theory of an attractor for nonlinear dynamics. Specifically, we first show that measuring the smoothness of a cross map between two observed variables can be used to detect a causal relation. Then, we provide a very effective algorithm to computationally evaluate the smoothness of the cross map, or "Cross Map Smoothness" (CMS), and thus to infer the causality, which can achieve high accuracy even with very short time series data. Analysis of both mathematical models from various benchmarks and real data from biological systems validates our method.

Convergent cross-mapping and pairwise asymmetric inference

Convergent cross-mapping (CCM) is a technique for computing specific kinds of correlations between sets of times series. It was introduced by Sugihara et al. [Science 338, 496 (2012).] and is reported to be "a necessary condition for causation" capable of distinguishing causality from standard correlation. We show that the relationships between CCM correlations proposed by Sugihara et al. do not, in general, agree with intuitive concepts of "driving" and as such should not be considered indicative of causality. It is shown that the fact that the CCM algorithm implies causality is a function of system parameters for simple linear and nonlinear systems. For example, in a circuit containing a single resistor and inductor, both voltage and current can be identified as the driver depending on the frequency of the source voltage. It is shown that the CCM algorithm, however, can be modified to identify relationships between pairs of time series that are consistent with intuition for the considered example systems for which CCM causality analysis provided nonintuitive driver identifications. This modification of the CCM algorithm is introduced as "pairwise asymmetric inference" (PAI) and examples of its use are presented.

Robust sequential working memory recall in heterogeneous cognitive networks

Psychiatric disorders are often caused by partial heterogeneous disinhibition in cognitive networks, controlling sequential and spatial working memory (SWM). Such dynamic connectivity changes suggest that the normal relationship between the neuronal components within the network deteriorates. As a result, competitive network dynamics is qualitatively altered. This dynamics defines the robust recall of the sequential information from memory and, thus, the SWM capacity. To understand pathological and non-pathological bifurcations of the sequential memory dynamics, here we investigate the model of recurrent inhibitory-excitatory networks with heterogeneous inhibition. We consider the ensemble of units with all-to-all inhibitory connections, in which the connection strengths are monotonically distributed at some interval. Based on computer experiments and studying the Lyapunov exponents, we observed and analyzed the new phenomenon—clustered sequential dynamics. The results are interpreted in the context of the winnerless competition principle. Accordingly, clustered sequential dynamics is represented in the phase space of the model by two weakly interacting quasi-attractors. One of them is similar to the sequential heteroclinic chain—the regular image of SWM, while the other is a quasi-chaotic attractor. Coexistence of these quasi-attractors means that the recall of the normal information sequence is intermittently interrupted by episodes with chaotic dynamics. We indicate potential dynamic ways for augmenting damaged working memory and other cognitive functions.

Model-free quantification of time-series predictability

This paper provides insight into when, why, and how forecast strategies fail when they are applied to complicated time series. We conjecture that the inherent complexity of real-world time-series data, which results from the dimension, nonlinearity, and nonstationarity of the generating process, as well as from measurement issues such as noise, aggregation, and finite data length, is both empirically quantifiable and directly correlated with predictability. In particular, we argue that redundancy is an effective way to measure complexity and predictive structure in an experimental time series and that weighted permutation entropy is an effective way to estimate that redundancy. To validate these conjectures, we study 120 different time-series data sets. For each time series, we construct predictions using a wide variety of forecast models, then compare the accuracy of the predictions with the permutation entropy of that time series. We use the results to develop a model-free heuristic that can help practitioners recognize when a particular prediction method is not well matched to the task at hand: that is, when the time series has more predictive structure than that method can capture and exploit.

Local Dynamic Stability of Spine Muscle Activation and Stiffness Patterns During Repetitive Lifting

To facilitate stable trunk kinematics, humans must generate appropriate motor patterns to effectively control muscle force and stiffness and respond to biomechanical perturbations and/or neuromuscular control errors. Thus, it is important to understand physiological variables such as muscle force and stiffness, and how these relate to the downstream production of stable spine and trunk movements. This study was designed to assess the local dynamic stability of spine muscle activation and rotational stiffness patterns using Lyapunov analyses, and relationships to the local dynamic stability of resulting spine kinematics, during repetitive lifting and lowering at varying combinations of lifting load and rate. With an increase in the load lifted at a constant rate there was a trend for decreased local dynamic stability of spine muscle activations and the muscular contributions to spine rotational stiffness; although the only significant change was for the full state space muscle activation stability (p < 0.05). With an increase in lifting rate with a constant load there was a significant decrease in the local dynamic stability of spine muscle activations and the muscular contributions to spine rotational stiffness (p ≤ 0.001 for all measures). These novel findings suggest that the stability of motor inputs and the muscular contributions to spine rotational stiffness can be altered by external task demands (load and lifting rate), and therefore are important variables to consider when assessing the stability of the resulting kinematics.

Association between Muscle Synergy and Stability during Prolonged Walking

[Purpose] The purpose of this study was to examine whether changes in muscle synergy could affect gait stability or muscle activity by comparing muscle activity before and after prolonged walking. [Subjects and Methods] Twelve healthy male subjects walked on a treadmill for 10 min as a warm-up. Data were recorded from the participants during the first and last 1 min during 90 min of walking at 4.5 km/h. Electromyographic (EMG) activity was recorded for 7 leg muscles, and patterns of coordination were determined by principal component analysis (PCA). The patterns of activity within the anatomic muscle groups were additionally determined by repeating PCA. iEMG was calculated using the mean EMG for each cycle step during the 1 min walking periods. The largest Lyapunov exponent was calculated to quantify each subject’s inherent local dynamic stability. [Results] The patterns for each of the 7 muscles showed no change between the start and end periods. However, the end period showed a higher co-activation of the triceps surae, lower iEMG of the medial gastrocnemius, and a smaller largest Lyapunov exponent of the mediolateral and anteroposterior directions than those observed during the start period. [Conclusion] The increase in triceps surae co-activation may be associated with gait stability.

Grouping feedback components by common fate benefits motor-respiratory coordination

The purpose of this study was to see how motor-respiratory coordination could improve with augmented visual feedback. Participants performed inphase and antiphase patterns between movement and breathing. When the target pattern was performed properly, balls in a feedback display either moved up and down together (inphase feedback) or opposite each other (antiphase feedback). Relative phase performance was less variable in the augmented feedback conditions than in a no display control condition. Within the augmented feedback conditions, variability was lower with inphase feedback than antiphase feedback. Cross-recurrence analysis was used to determine whether other changes occurred on shorter time scales. On cross-recurrence measures, performance was more variable with inphase feedback than in the control condition and with antiphase feedback. Those results suggest that, with inphase feedback, participants were able to achieve more stable overall relative phase patterns using small within-cycle trajectory changes. Those small changes were possible because the balls in the inphase feedback display were grouped by common fate. That perceptual organization made it possible for participants to see slight mismatches between movement and breathing and control coordination accordingly.

Dancers entrain more effectively than non-dancers to another actor's movements

For many everyday sensorimotor tasks, trained dancers have been found to exhibit distinct and sometimes superior (more stable or robust) patterns of behavior compared to non-dancers. Past research has demonstrated that experts in fields requiring specialized physical training and behavioral control exhibit superior interpersonal coordination capabilities for expertise-related tasks. To date, however, no published studies have compared dancers' abilities to coordinate their movements with the movements of another individual-i.e., during a so-called visual-motor interpersonal coordination task. The current study was designed to investigate whether trained dancers would be better able to coordinate with a partner performing short sequences of dance-like movements than non-dancers. Movement time series were recorded for individual dancers and non-dancers asked to synchronize with a confederate during three different movement sequences characterized by distinct dance styles (i.e., dance team routine, contemporary ballet, mixed style) without hearing any auditory signals or music. A diverse range of linear and non-linear analyses (i.e., cross-correlation, cross-recurrence quantification analysis, and cross-wavelet analysis) provided converging measures of coordination across multiple time scales. While overall levels of interpersonal coordination were influenced by differences in movement sequence for both groups, dancers consistently displayed higher levels of coordination with the confederate at both short and long time scales. These findings demonstrate that the visual-motor coordination capabilities of trained dancers allow them to better synchronize with other individuals performing dance-like movements than non-dancers. Further investigation of similar tasks may help to increase the understanding of visual-motor entrainment in general, as well as provide insight into the effects of focused training on visual-motor and interpersonal coordination.

Experimental dynamical characterization of five autonomous chaotic oscillators with tunable series resistance

In this paper, an experimental characterization of the dynamical properties of five autonomous chaotic oscillators, based on bipolar-junction transistors and obtained de-novo through a genetic algorithm in a previous study, is presented. In these circuits, a variable resistor connected in series to the DC voltage source acts as control parameter, for a range of which the largest Lyapunov exponent, correlation dimension, approximate entropy, and amplitude variance asymmetry are calculated, alongside bifurcation diagrams and spectrograms. Numerical simulations are compared to experimental measurements. The oscillators can generate a considerable variety of regular and chaotic sine-like and spike-like signals.

Information-transmission rates in manual control of unstable systems with time delays

In analyzing the human-machine interaction (HMI), a human-centered approach is needed to address the potential and limitation of human control, especially in the control of high-order or unstable systems. However, there is no quantitative measure of the human performance or cognitive workload in these difficult HMI tasks. We propose to characterize the HMI as information flows quantified by the information-transmission rate in bits per second (b/s). Using information- and control-theoretic approaches, we derive the minimum rates of information transmission in manual control required by any deterministic controller to stabilize the feedback system. Furthermore, we suggest a method adopted from time-series analysis to estimate the information-transmission rate from human experiments. We show that the relationship between the empirically estimated information rates and the minimum bounds allows for the quantitative indication of the potential and limitation of human manual control. We illustrate our method in the control of an inverted pendulum with time delays.

Change in the embedding dimension as an indicator of an approaching transition

Predicting a transition point in behavioral data should take into account the complexity of the signal being influenced by contextual factors. In this paper, we propose to analyze changes in the embedding dimension as contextual information indicating a proceeding transitive point, called OPtimal Embedding tRANsition Detection (OPERAND). Three texts were processed and translated to time-series of emotional polarity. It was found that changes in the embedding dimension proceeded transition points in the data. These preliminary results encourage further research into changes in the embedding dimension as generic markers of an approaching transition point.

Could local dynamic stability serve as an early predictor of falls in patients with moderate neurological gait disorders? A reliability and comparison study in healthy individuals and in patients with paresis of the lower extremities

Falls while walking are frequent in patients with muscular dysfunction resulting from neurological disorders. Falls induce injuries that may lead to deconditioning and disabilities, which further increase the risk of falling. Therefore, an early gait stability index would be useful to evaluate patients in order to prevent the occurrence of future falls. Derived from chaos theory, local dynamic stability (LDS), defined by the maximal Lyapunov exponent, assesses the sensitivity of a dynamic system to small perturbations. LDS has already been used for fall risk prediction in elderly people. The aim of the present study was to provide information to facilitate future researches regarding gait stability in patients with neurological gait disorders. The main objectives were 1) to evaluate the intra-session repeatability of LDS in patients and 2) to assess the discriminative power of LDS to differentiate between healthy individuals and neurological patients. Eighty-three patients with mild to moderate neurological disorders associated with paresis of the lower extremities and 40 healthy controls participated in the study. The participants performed 2×30 s walking wearing a 3D accelerometer attached to the lower back, from which 2×35 steps were extracted. LDS was defined as the average exponential rate of divergence among trajectories in a reconstructed state-space that reflected the gait dynamics. LDS assessed along the medio-lateral axis offered the highest repeatability and discriminative power. Intra-session repeatability (intraclass correlation coefficient between the two repetitions) in the patients was 0.89 and the smallest detectable difference was 16%. LDS was substantially lower in the patients than in the controls (33% relative difference, standardized effect size 2.3). LDS measured in short over-ground walking tests seems sufficiently reliable. LDS exhibits good discriminative power to differentiate fall-prone individuals and opens up the possibility of future clinical applications for better prediction of fall risk in neurological patients.

Nonlinear analyses of elicited modal, raised, and pressed rabbit phonation

OBJECTIVES/HYPOTHESIS

The purpose of this study was to use nonlinear dynamic analysis methods such as phase space portraits and correlation dimension (D2) as well as descriptive spectrographic analyses to characterize acoustic signals produced during evoked rabbit phonation.

METHODS

Seventeen New Zealand white breeder rabbits were used to perform the study. A Grass S-88 stimulator (SA Instrumentation, Encinitas, CA) and constant current isolation unit (Grass Telefactor, model PSIU6; West Warwick, RI) were used to provide electrical stimulation to laryngeal musculature, and transglottal airflow rate and stimulation current (mA) were manipulated to elicit modal, raised intensity, and pressed phonations. Central 1 second portions of the most stable portion of the acoustic waveform for modal, raised intensity, and pressed phonations were edited and then analyzed via phase space portraits, Poincaré sections, and the estimation of the D2. In an attempt to limit the effects of the highly variable and nonstationary characteristics of some of the signals being analyzed, D2 analysis was also performed on the most stable central 200-millisecond portion of the acoustic waveform. Descriptive analysis of each phonation was also conducted using sound spectrograms.

RESULTS

Results showed that the complexity of phonation and the subsequent acoustic waveform is increased as transglottal airflow rate and degree of glottal adduction are manipulated in the evoked rabbit phonation model. In particular, phonatory complexity, as quantified via D2 analyses and demonstrated via spectrographic characteristics, increases from "modal" (ie, phonation elicited at just above the phonation threshold pressure) to raised intensity (phonation elicited by increasing transglottal airflow rate) to pressed (phonation elicited by increasing the stimulation current delivered to the larynx). Variations in a single dynamic dimension (airflow rate or adductory force) resulted in significantly increased productions of nonlinear phenomenon, including bifurcations from periodicity to regions of subharmonic content, fundamental frequency, and harmonic jumps, and evidence of periodicity within aperiodic regions ("chaos").

CONCLUSIONS

The evoked rabbit phonation model described in this study allows for the elicitation of various types of phonations under controlled conditions and, therefore, has the potential to provide insight regarding important variables that may elicit examples of nonlinear phenomena such as subharmonics and deterministic chaos.

Visual influences on postural and manual interpersonal coordination during a joint precision task

We investigated whether the interpersonal postural coordination that occurs during a joint supra-postural, manual precision task is driven by the constraints of the task, or, instead results from visual entrainment to the movements of a co-actor. Participants were instructed to coordinate their finger movements under conditions where participants could see others' whole-body movements or could only see the results of the other's actions. Participants' finger and torso movements were recorded. Coordination was quantified using cross-recurrence quantification analysis measures. Interpersonal coordination was enhanced by, although it did not depend entirely upon, visual information about the co-actor's body movements.