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

Chaos of radiative heat-loss-induced flame front instability

We are intensively studying the chaos via the period-doubling bifurcation cascade in radiative heat-loss-induced flame front instability by analytical methods based on dynamical systems theory and complex networks. Significant changes in flame front dynamics in the chaotic region, which cannot be seen in the bifurcation diagrams, were successfully extracted from recurrence quantification analysis and nonlinear forecasting and from the network entropy. The temporal dynamics of the fuel concentration in the well-developed chaotic region is much more complicated than that of the flame front temperature. It exhibits self-affinity as a result of the scale-free structure in the constructed visibility graph.

Complexity in congestive heart failure: A time-frequency approach

Reconstruction of phase space is an effective method to quantify the dynamics of a signal or a time series. Various phase space reconstruction techniques have been investigated. However, there are some issues on the optimal reconstructions and the best possible choice of the reconstruction parameters. This research introduces the idea of gradient cross recurrence (GCR) and mean gradient cross recurrence density which shows that reconstructions in time frequency domain preserve more information about the dynamics than the optimal reconstructions in time domain. This analysis is further extended to ECG signals of normal and congestive heart failure patients. By using another newly introduced measure-gradient cross recurrence period density entropy, two classes of aforesaid ECG signals can be classified with a proper threshold. This analysis can be applied to quantifying and distinguishing biomedical and other nonlinear signals.

Leveraging information storage to select forecast-optimal parameters for delay-coordinate reconstructions

Delay-coordinate reconstruction is a proven modeling strategy for building effective forecasts of nonlinear time series. The first step in this process is the estimation of good values for two parameters, the time delay and the embedding dimension. Many heuristics and strategies have been proposed in the literature for estimating these values. Few, if any, of these methods were developed with forecasting in mind, however, and their results are not optimal for that purpose. Even so, these heuristics-intended for other applications-are routinely used when building delay coordinate reconstruction-based forecast models. In this paper, we propose an alternate strategy for choosing optimal parameter values for forecast methods that are based on delay-coordinate reconstructions. The basic calculation involves maximizing the shared information between each delay vector and the future state of the system. We illustrate the effectiveness of this method on several synthetic and experimental systems, showing that this metric can be calculated quickly and reliably from a relatively short time series, and that it provides a direct indication of how well a near-neighbor based forecasting method will work on a given delay reconstruction of that time series. This allows a practitioner to choose reconstruction parameters that avoid any pathologies, regardless of the underlying mechanism, and maximize the predictive information contained in the reconstruction.

Analysis of dual-task elderly gait in fallers and non-fallers using wearable sensors

Dual-task (DT) gait involves walking while simultaneously performing an attention-demanding task and can be used to identify impaired gait or executive function in older adults. Advancment is needed in techniques that quantify the influence of dual tasking to improve predictive and diagnostic potential. This study investigated the viability of wearable sensor measures to identify DT gait changes in older adults and distinguish between elderly fallers and non-fallers. A convenience sample of 100 older individuals (75.5±6.7 years; 76 non-fallers, 24 fallers based on 6 month retrospective fall occurrence) walked 7.62m under single-task (ST) and DT conditions while wearing pressure-sensing insoles and tri-axial accelerometers at the head, pelvis, and left and right shanks. Differences between ST and DT gait were identified for temporal measures, acceleration descriptive statistics, Fast Fourier Transform (FFT) quartiles, ratio of even to odd harmonics, center of pressure (CoP) stance path coefficient of variation, and deviations to expected CoP stance path. Increased posterior CoP stance path deviations, increased coefficient of variation, decreased FFT quartiles, and decreased ratio of even to odd harmonics suggested increased DT gait variability. Decreased gait velocity and decreased acceleration standard deviations (SD) at the pelvis and shanks could represent compensatory gait strategies that maintain stability. Differences in acceleration between fallers and non-fallers in head posterior SD and pelvis AP ratio of even to odd harmonics during ST, and pelvis vertical maximum Lyapunov exponent during DT gait were identified. Wearable-sensor-based DT gait assessments could be used in point-of-care environments to identify gait deficits.

The reliability of local dynamic stability in walking while texting and performing an arithmetical problem

In the recent years, local dynamic stability of walking was frequently used to quantify motor control. Particularly, dual-task paradigms are used to assess a shift in gait control strategy to test walking in real life situations. Texting short messages while walking is a common motor-cognitive dual task of daily living. To able to monitor possible intervention effects on motor-cognitive dual-task performance, the test-retest reliability of the measure has to be evaluated. Since the reliability of the effects of cognitive tasks including texting while walking on local dynamic gait stability has not been assessed yet, this will be evaluated in the current study. Eleven young individuals were included. Gait data was registered twice (test-retest interval: seven days) using an inertial sensor fixed on the subjects' trunks in three conditions: normal walking, walking while texting a message and walking while reciting serials of 7. Short-term finite maximum Lyapunov Exponents were quantified to assess local dynamic stability. The test-retest reliability was calculated using intra-class correlation coefficients and Bland and Altman Plots (bias and limits of agreement). ICC values of the current study show that in normal walking and walking while texting, outcomes are comparable and indicate mostly good to excellent reliability. The reliability values were almost always the lowest in walking while reciting serials of 7. Local dynamic stability derived from kinematic data of walking while cell phone texting can be reliably collected and, in turn, be used as an outcome measure in clinical trials with repeated measures design.

Classification of Asthma Based on Nonlinear Analysis of Breathing Pattern

Normal human breathing exhibits complex variability in both respiratory rhythm and volume. Analyzing such nonlinear fluctuations may provide clinically relevant information in patients with complex illnesses such as asthma. We compared the cycle-by-cycle fluctuations of inter-breath interval (IBI) and lung volume (LV) among healthy volunteers and patients with various types of asthma. Continuous respiratory datasets were collected from forty age-matched men including 10 healthy volunteers, 10 patients with controlled atopic asthma, 10 patients with uncontrolled atopic asthma, and 10 patients with uncontrolled non-atopic asthma during 60 min spontaneous breathing. Complexity of breathing pattern was quantified by calculating detrended fluctuation analysis, largest Lyapunov exponents, sample entropy, and cross-sample entropy. The IBI as well as LV fluctuations showed decreased long-range correlation, increased regularity and reduced sensitivity to initial conditions in patients with asthma, particularly in uncontrolled state. Our results also showed a strong synchronization between the IBI and LV in patients with uncontrolled asthma. Receiver operating characteristic (ROC) curve analysis showed that nonlinear analysis of breathing pattern has a diagnostic value in asthma and can be used in differentiating uncontrolled from controlled and non-atopic from atopic asthma. We suggest that complexity analysis of breathing dynamics may represent a novel physiologic marker to facilitate diagnosis and management of patients with asthma. However, future studies are needed to increase the validity of the study and to improve these novel methods for better patient management.

Effect of filtering on the classification rate of nonlinear analysis methods applied to uterine EMG signals

Nonlinear time series analysis can provide useful information regarding nonlinear features of biological signals. The effect of filtering on the performance of nonlinear methods is not well-understood. In this work, we investigate the effects of signal filtering on the sensitivity of four nonlinear methods: Time reversibility, Sample Entropy, Lyapunov Exponents and Delay Vector Variance. These methods were applied to uterine EMG signals with the aim of using them to discriminate between pregnancy and labor contractions. The signals were filtered using three different band-pass filters before the application of the methods. Results showed that the sensitivity of some methods such as sample entropy was significantly improved with filtering. On the other hand, filtering had little effect on some other methods such as time reversibility. This study concludes that while filtering increases computation time, it may be necessary for some nonlinear methods particularly those with low sensitivity.

Significance of using a nonlinear analysis technique, the Lyapunov exponent, on the understanding of the dynamics of the cardiorespiratory system in rats

BACKGROUND/AIM

Pneumocardiography (PNCG) is the recording method of cardiac-induced tracheal air flow and pressure pulsations in the respiratory airways. PNCG signals reflect both the lung and heart actions and could be accurately recorded in spontaneously breathing anesthetized rats. Nonlinear analysis methods, including the Lyapunov exponent, can be used to explain the biological dynamics of systems such as the cardiorespiratory system.

MATERIALS AND METHODS

In this study, we recorded tracheal air flow signals, including PNCG signals, from 3 representative anesthetized rats and analyzed the nonlinear behavior of these complex signals using Lyapunov exponents.

RESULTS

Lyapunov exponents may also be used to determine the normal and pathological structure of biological systems. If the signals have at least one positive Lyapunov exponent, the signals reflect chaotic activity, as seen in PNCG signals in rats; the largest Lyapunov exponents of the signals of the healthy rats were greater than zero in this study.

CONCLUSION

A method was proposed to determine the diagnostic and prognostic values of the cardiorespiratory system of rats using the arrangement of the PNCG and Lyapunov exponents, which may be monitored as vitality indicators.

A comprehensive study of the delay vector variance method for quantification of nonlinearity in dynamical systems

Although vibration monitoring is a popular method to monitor and assess dynamic structures, quantification of linearity or nonlinearity of the dynamic responses remains a challenging problem. We investigate the delay vector variance (DVV) method in this regard in a comprehensive manner to establish the degree to which a change in signal nonlinearity can be related to system nonlinearity and how a change in system parameters affects the nonlinearity in the dynamic response of the system. A wide range of theoretical situations are considered in this regard using a single degree of freedom (SDOF) system to obtain numerical benchmarks. A number of experiments are then carried out using a physical SDOF model in the laboratory. Finally, a composite wind turbine blade is tested for different excitations and the dynamic responses are measured at a number of points to extend the investigation to continuum structures. The dynamic responses were measured using accelerometers, strain gauges and a Laser Doppler vibrometer. This comprehensive study creates a numerical and experimental benchmark for structurally dynamical systems where output-only information is typically available, especially in the context of DVV. The study also allows for comparative analysis between different systems driven by the similar input.

Prediction in projection

Prediction models that capture and use the structure of state-space dynamics can be very effective. In practice, however, one rarely has access to full information about that structure, and accurate reconstruction of the dynamics from scalar time-series data-e.g., via delay-coordinate embedding-can be a real challenge. In this paper, we show that forecast models that employ incomplete reconstructions of the dynamics-i.e., models that are not necessarily true embeddings-can produce surprisingly accurate predictions of the state of a dynamical system. In particular, we demonstrate the effectiveness of a simple near-neighbor forecast technique that works with a two-dimensional time-delay reconstruction of both low- and high-dimensional dynamical systems. Even though correctness of the topology may not be guaranteed for incomplete reconstructions like this, the dynamical structure that they do capture allows for accurate predictions-in many cases, even more accurate than predictions generated using a traditional embedding. This could be very useful in the context of real-time forecasting, where the human effort required to produce a correct delay-coordinate embedding is prohibitive.

Remote synchronization of amplitudes across an experimental ring of non-linear oscillators

In this paper, the emergence of remote synchronization in a ring of 32 unidirectionally coupled non-linear oscillators is reported. Each oscillator consists of 3 negative voltage gain stages connected in a loop to which two integrators are superimposed and receives input from its preceding neighbour via a "mixing" stage whose gains form the main system control parameters. Collective behaviour of the network is investigated numerically and experimentally, based on a custom-designed circuit board featuring 32 field-programmable analog arrays. A diverse set of synchronization patterns is observed depending on the control parameters. While phase synchronization ensues globally, albeit imperfectly, for certain control parameter values, amplitudes delineate subsets of non-adjacent but preferentially synchronized nodes; this cannot be trivially explained by synchronization paths along sequences of structurally connected nodes and is therefore interpreted as representing a form of remote synchronization. Complex topology of functional synchronization thus emerges from underlying elementary structural connectivity. In addition to the Kuramoto order parameter and cross-correlation coefficient, other synchronization measures are considered, and preliminary findings suggest that generalized synchronization may identify functional relationships across nodes otherwise not visible. Further work elucidating the mechanism underlying this observation of remote synchronization is necessary, to support which experimental data and board design materials have been made freely downloadable.

Reconstructing the micrometeorological dynamics of the southern Amazonian transitional forest

In this work, we reconstruct and analyze the micrometeorological dynamics of the transitional forest located south of the Amazon basin. For this, we use time series of micrometeorological variables collected over five years in the transitional forest of Mato Grosso (Brazil). We employ local feature analysis, a recently proposed extension of principal component analysis, to extract the most relevant physical variables from this set. We show in this way that temperature records contain most of the dynamical information in all seasons. Based on this result, the dimensionality of the space spanned by the system's dynamics and the properties of the so defined attractors are obtained. In the dry season, the system presents a robust oscillatory character described by a well-defined limit cycle. In the wet season, the dynamics becomes more irregular but can still be seen as a periodic behavior affected by external noise. These results can help to develop accurate models for the meteorology of the Amazonian transitional forest and can thus lead to a better understanding of this important ecosystem.

Visibility Graph Based Time Series Analysis

Network based time series analysis has made considerable achievements in the recent years. By mapping mono/multivariate time series into networks, one can investigate both it's microscopic and macroscopic behaviors. However, most proposed approaches lead to the construction of static networks consequently providing limited information on evolutionary behaviors. In the present paper we propose a method called visibility graph based time series analysis, in which series segments are mapped to visibility graphs as being descriptions of the corresponding states and the successively occurring states are linked. This procedure converts a time series to a temporal network and at the same time a network of networks. Findings from empirical records for stock markets in USA (S&P500 and Nasdaq) and artificial series generated by means of fractional Gaussian motions show that the method can provide us rich information benefiting short-term and long-term predictions. Theoretically, we propose a method to investigate time series from the viewpoint of network of networks.

Wearing a Wetsuit Alters Upper Extremity Motion during Simulated Surfboard Paddling

Surfers often wear wetsuits while paddling in the ocean. This neoprene covering may be beneficial to upper extremity movement by helping to improve proprioceptive acuity, or it may be detrimental by providing increased resistance. The purpose of this study was to evaluate the effects of wearing a wetsuit on muscle activation, upper extremity motion, heart rate, and oxygen consumption during simulated surfboard paddling in the laboratory. Twelve male, recreational surfers performed two paddling trials at a constant workload on a swim bench ergometer both with and without a wetsuit. Kinematic data and EMG were acquired from the right arm via motion capture, and oxygen consumption and heart rate were recorded with a metabolic cart and heart rate monitor. Wearing a wetsuit had no significant effect on oxygen consumption or heart rate. A significant increase in EMG activation was observed for the middle deltoid but not for any of the other shoulder muscle evaluated. Finally, approximate entropy and estimates of the maximum Lyapunov exponent increased significantly for vertical trajectory of the right wrist (i.e. stroke height) when a wetsuit was worn. These results suggest that a 2mm wetsuit has little effect on the energy cost of paddling at lower workloads but does affect arm motion. These changes may be the result of enhanced proprioceptive acuity due to mechanical compression from the wetsuit.

Untangling Brain-Wide Dynamics in Consciousness by Cross-Embedding

Brain-wide interactions generating complex neural dynamics are considered crucial for emergent cognitive functions. However, the irreducible nature of nonlinear and high-dimensional dynamical interactions challenges conventional reductionist approaches. We introduce a model-free method, based on embedding theorems in nonlinear state-space reconstruction, that permits a simultaneous characterization of complexity in local dynamics, directed interactions between brain areas, and how the complexity is produced by the interactions. We demonstrate this method in large-scale electrophysiological recordings from awake and anesthetized monkeys. The cross-embedding method captures structured interaction underlying cortex-wide dynamics that may be missed by conventional correlation-based analysis, demonstrating a critical role of time-series analysis in characterizing brain state. The method reveals a consciousness-related hierarchy of cortical areas, where dynamical complexity increases along with cross-area information flow. These findings demonstrate the advantages of the cross-embedding method in deciphering large-scale and heterogeneous neuronal systems, suggesting a crucial contribution by sensory-frontoparietal interactions to the emergence of complex brain dynamics during consciousness.

Characterization of degeneration process in combustion instability based on dynamical systems theory

We present a detailed study on the characterization of the degeneration process in combustion instability based on dynamical systems theory. We deal with combustion instability in a lean premixed-type gas-turbine model combustor, one of the fundamentally and practically important combustion systems. The dynamic behavior of combustion instability in close proximity to lean blowout is dominated by a stochastic process and transits to periodic oscillations created by thermoacoustic combustion oscillations via chaos with increasing equivalence ratio [Chaos 21, 013124 (2011); Chaos 22, 043128 (2012)]. Thermoacoustic combustion oscillations degenerate with a further increase in the equivalence ratio, and the dynamic behavior leads to chaotic fluctuations via quasiperiodic oscillations. The concept of dynamical systems theory presented here allows us to clarify the nonlinear characteristics hidden in complex combustion dynamics.

Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.

Parsimonious description for predicting high-dimensional dynamics

When we observe a system, we often cannot observe all its variables and may have some of its limited measurements. Under such a circumstance, delay coordinates, vectors made of successive measurements, are useful to reconstruct the states of the whole system. Although the method of delay coordinates is theoretically supported for high-dimensional dynamical systems, practically there is a limitation because the calculation for higher-dimensional delay coordinates becomes more expensive. Here, we propose a parsimonious description of virtually infinite-dimensional delay coordinates by evaluating their distances with exponentially decaying weights. This description enables us to predict the future values of the measurements faster because we can reuse the calculated distances, and more accurately because the description naturally reduces the bias of the classical delay coordinates toward the stable directions. We demonstrate the proposed method with toy models of the atmosphere and real datasets related to renewable energy.

Quantifying foot placement variability and dynamic stability of movement to assess control mechanisms during forward and lateral running

Research has indicated that human walking is more unstable in the secondary, rather than primary plane of progression. However, the mechanisms of controlling dynamic stability in different planes of progression during running remain unknown. The aim of this study was to compare variability (standard deviation and coefficient of variation) and dynamic stability (sample entropy and local divergence exponent) in anterior-posterior and medio-lateral directions in forward and lateral running patterns. For this purpose, fifteen healthy, male participants ran in a forward and lateral direction on a treadmill at their preferred running speeds. Coordinate data of passive reflective markers attached to body segments were recorded using a motion capture system. Results indicated that: (1) there is lower dynamic stability in the primary plane of progression during both forward and lateral running suggesting that, unlike walking, greater control might be required to regulate dynamic stability in the primary plane of progression during running, (2) as in walking, the control of stability in anterior-posterior and medio-lateral directions of running is dependent on the direction of progression, and (3), quantifying magnitude of variability might not be sufficient to understand control mechanisms in human movement and directly measuring dynamic stability could be an appropriate alternative.

Low-dimensional attractor for neural activity from local field potentials in optogenetic mice

We used optogenetic mice to investigate possible nonlinear responses of the medial prefrontal cortex (mPFC) local network to light stimuli delivered by a 473 nm laser through a fiber optics. Every 2 s, a brief 10 ms light pulse was applied and the local field potentials (LFPs) were recorded with a 10 kHz sampling rate. The experiment was repeated 100 times and we only retained and analyzed data from six animals that showed stable and repeatable response to optical stimulations. The presence of nonlinearity in our data was checked using the null hypothesis that the data were linearly correlated in the temporal domain, but were random otherwise. For each trail, 100 surrogate data sets were generated and both time reversal asymmetry and false nearest neighbor (FNN) were used as discriminating statistics for the null hypothesis. We found that nonlinearity is present in all LFP data. The first 0.5 s of each 2 s LFP recording were dominated by the transient response of the networks. For each trial, we used the last 1.5 s of steady activity to measure the phase resetting induced by the brief 10 ms light stimulus. After correcting the LFPs for the effect of phase resetting, additional preprocessing was carried out using dendrograms to identify “similar” groups among LFP trials. We found that the steady dynamics of mPFC in response to light stimuli could be reconstructed in a three-dimensional phase space with topologically similar “8”-shaped attractors across different animals. Our results also open the possibility of designing a low-dimensional model for optical stimulation of the mPFC local network.

Effects of noxious stimulation to the back or calf muscles on gait stability

Gait stability is the ability to deal with small perturbations that naturally occur during walking. Changes in motor control caused by pain could affect this ability. This study investigated whether nociceptive stimulation (hypertonic saline injection) in a low back (LBP) or calf (CalfP) muscle affects gait stability. Sixteen participants walked on a treadmill at 0.94ms(-1) and 1.67ms(-1), while thorax kinematics were recorded using 3D-motion capture. From 110 strides, stability (local divergence exponent, LDE), stride-to-stride variability and root mean squares (RMS) of thorax linear velocities were calculated along the three movement axes. At 0.94ms(-1), independent of movement axes, gait stability was lower (higher LDE) and stride-to-stride variability was higher, during LBP and CalfP than no pain. This was more pronounced during CalfP, likely explained by the biomechanical function of calf muscles in gait, as supported by greater mediolateral RMS and stance time asymmetry than in LBP and no pain. At 1.67ms(-1), independent of movement axes, gait stability was greater and stride-to-stride variability was smaller with LBP than no pain and CalfP, whereas CalfP was not different from no pain. Opposite effects of LBP on gait stability between speeds suggests a more protective strategy at the faster speed. Although mediolateral RMS was greater and participants had more asymmetric stance times with CalfP than LBP and no pain, limited effect of CalfP at the faster speed could relate to greater kinematic constraints and smaller effects of calf muscle activity on propulsion at this speed. In conclusion, pain effects on gait stability depend on pain location and walking speed.

Lost in the Rhythm: Effects of Rhythm on Subsequent Interpersonal Coordination

Music is a natural human expression present in all cultures, but the functions it serves are still debated. Previous research indicates that rhythm, an essential feature of music, can enhance coordination of movement and increase social bonding. However, the prolonged effects of rhythm have not yet been investigated. In this study, pairs of participants were exposed to one of three kinds of auditory stimuli (rhythmic, arrhythmic, or white-noise) and subsequently engaged in five trials of a joint-action task demanding interpersonal coordination. We show that when compared with the other two stimuli, exposure to the rhythmic beat reduced the practice effect in task performance. Analysis of the behavioral data suggests that this reduction results from more temporally coupled motor movements over successive trials and that shared exposure to rhythm facilitates interpersonal motor coupling, which in this context serves to impede the attainment of necessary dynamic coordination. We propose that rhythm has the potential to enhance interpersonal motor coupling, which might serve as a mechanism behind its facilitation of positive social attitudes.

Does visual augmented feedback reduce local dynamic stability while walking?

Augmented feedback is frequently used in gait training to efficiently correct specific gait patterns in patients with different disorders. The patients use this external augmented feedback to align actual movements in a way that predefined gait characteristics can be achieved. Voluntary changes of gait characteristics are reported to reduce local dynamic stability (LDS) which in turn is associated with increased risk of falling. The aim of this study was to evaluate the instantaneous effect of visual feedback, provided to help patients to correct frontal plane pelvis and trunk movements, on the LDS of pelvis and trunk. Kinematic gait data was captured in ten women with gait disorders. The effect of visual feedback on LDS, quantified with the largest Lyapunov exponent, of walking was examined. We found a significant decreased LDS (e.g. pelvis: p=.009) in our subjects when they were using visual augmented feedback. Our data suggest that the use of visual augmented feedback causes less stable gait patterns indicating a reduced ability to respond to small perturbations which might increase risk of falling. Therefore, researchers or clinicians who aim to correct gait patterns through real time based external augmented feedback should consider the potential negative effect on gait stability. It should be evaluated if the possible increased fall risk provoked by visual feedback exceeds possible increases in fall risk induced by conventional gait-retraining interventions. The external validity of the study is limited because of the low sample size and inhomogeneous group characteristics. Thus, further studies including homogeneous cohorts are required.

A study of human colonic motility in healthy and constipated subjects using the wireless capsule

Constipation is a common and distressing condition that has been linked to major morbidity, burdens the health care system, and impacts patients׳ quality of life. However, there is no perfect method for diagnosing and treating constipation. The purpose of this paper is to develop an automatic algorithm to identify patients with constipation from healthy subjects. Data from 12 healthy subjects and 10 patients with constipation were analyzed. The key challenges for data processing were data filtering, feature extraction, information evaluation, and providing the reference conclusion; these were resolved by employing the phase space reconstruction (PSR), independent component analysis (ICA), dynamic feature extraction algorithm, and the Wilcoxon rank sum test. The contractile frequency (Fr), motility index per unit time (MIU), average peak of peristaltic wave (Pave) and variance (Var) were extracted as dynamic parameters and analyzed. Results between groups were compared with the Wilcoxon rank sum test. There were statistically significant differences between healthy subjects and patients with constipation for Fr and MIU (P<0.05), whereas there was no statistically difference for Var. Moreover, the Fr and MIU of patients with normal transit constipation (NTC) are significantly lower compared to healthy subjects, whereas patients with slow transit constipation (STC) did not show significant differences. The proposed algorithms were able to differentiate between healthy subjects and patients with constipation based on the colonic motility profiles.

On the dynamics of ocean ambient noise: Two decades later

Two decades ago, it was shown that ambient noise exhibits low dimensional chaotic behavior. Recent new techniques in nonlinear science can effectively detect the underlying dynamics in noisy time series. In this paper, the presence of low dimensional deterministic dynamics in ambient noise is investigated using diverse nonlinear techniques, including correlation dimension, Lyapunov exponent, nonlinear prediction, and entropy based methods. The consistent interpretation of different methods demonstrates that ambient noise can be best modeled as nonlinear stochastic dynamics, thus rejecting the hypothesis of low dimensional chaotic behavior. The ambient noise data utilized in this study are of duration 60 s measured at South China Sea.

Gait variability and motor control in people with knee osteoarthritis

Knee osteoarthritis (OA) is a common disease that impairs walking ability and function. We compared the temporal gait variability and motor control in people with knee OA with healthy controls. The purpose was to test the hypothesis that the temporal gait variability would reflect a more stereotypic pattern in people with knee OA compared with healthy age-matched subjects. To assess the gait variability the temporal structure of the ankle and knee joint kinematics was quantified by the largest Lyapunov exponent and the stride time fluctuations were quantified by sample entropy and detrended fluctuation analysis. The motor control was assessed by the soleus (SO) Hoffmann (H)-reflex modulation and muscle co-activation during walking. The results showed no statistically significant mean group differences in any of the gait variability measures or muscle co-activation levels. The SO H-reflex amplitude was significantly higher in the knee OA group around heel strike when compared with the controls. The mean group difference in the H-reflex in the initial part of the stance phase (control-knee OA) was -6.6% Mmax (95% CI: -10.4 to -2.7, p=0.041). The present OA group reported relatively small impact of their disease. These results suggest that the OA group in general sustained a normal gait pattern with natural variability but with suggestions of facilitated SO H-reflex in the swing to stance phase transition. We speculate that the difference in SO H-reflex modulation reflects that the OA group increased the excitability of the soleus stretch reflex as a preparatory mechanism to avoid sudden collapse of the knee joint which is not uncommon in knee OA.

Dynamic trajectory of multiple single-unit activity during working memory task in rats

Working memory plays an important role in complex cognitive tasks. A popular theoretical view is that transient properties of neuronal dynamics underlie cognitive processing. The question raised here as to how the transient dynamics evolve in working memory. To address this issue, we investigated the multiple single-unit activity dynamics in rat medial prefrontal cortex (mPFC) during a Y-maze working memory task. The approach worked by reconstructing state space from delays of the original single-unit firing rate variables, which were further analyzed using kernel principal component analysis (KPCA). Then the neural trajectories were obtained to visualize the multiple single-unit activity. Furthermore, the maximal Lyapunov exponent (MLE) was calculated to quantitatively evaluate the neural trajectories during the working memory task. The results showed that the neuronal activity produced stable and reproducible neural trajectories in the correct trials while showed irregular trajectories in the incorrect trials, which may establish a link between the neurocognitive process and behavioral performance in working memory. The MLEs significantly increased during working memory in the correctly performed trials, indicating an increased divergence of the neural trajectories. In the incorrect trials, the MLEs were nearly zero and remained unchanged during the task. Taken together, the trial-specific neural trajectory provides an effective way to track the instantaneous state of the neuronal population during the working memory task and offers valuable insights into working memory function. The MLE describes the changes of neural dynamics in working memory and may reflect different neuronal population states in working memory.

Evaluation of an Expanded Disability Status Scale (EDSS) modeling strategy in multiple sclerosis

The Expanded Disability Status Scale (EDSS) is the most widely used scale to evaluate the degree of neurological impairment in multiple sclerosis (MS). In this paper, we report on the evaluation of an EDSS modeling strategy based on recurrence quantification analysis (RQA) of posturographic data (i.e., center of pressure, COP). A total of 133 volunteers with EDSS ranging from 0 to 4.5 participated in this study, with eyes closed. After selection of time delay (τ), embedding dimension (m) as well as threshold (radius, r) to identify recurrent points, several RQA measures were calculated for each COP's position and velocity data in the mono- and multi-dimensional RQAs. Estimation results lead to the selection of the recurrence rate (RR) of the COP's position as the most pertinent RQA measure. The performance of the models versus raw and noisy data was higher in the mono-dimensional analysis than in the multi-dimensional. This study suggests that the posturographic signal's mono-dimensional RQA is a more pertinent method to quantify disability in MS than the multi-dimensional RQA.

Local Dynamic Joint Stability During Human Treadmill Walking in Response to Lower Limb Segmental Loading Perturbations

Our purpose was to quantify changes in local dynamic stability (LDS) of the lumbar spine, hip, knee, and ankle in response to changes in lower limb segment mass, as well as to quantify temporal adaptations to segment loading during treadmill walking. Results demonstrate that increased mass distal to a joint yields either the maintenance of, or increased stabilization of, that particular joint relative to the unloaded condition. Increased mass proximal to a particular joint resulted in joint destabilization. The hip and ankle LDS were observed to change temporally, independent of segment loading condition, suggesting adaptation to walking on a treadmill interface.

Complex network based techniques to identify extreme events and (sudden) transitions in spatio-temporal systems

We present here two promising techniques for the application of the complex network approach to continuous spatio-temporal systems that have been developed in the last decade and show large potential for future application and development of complex systems analysis. First, we discuss the transforming of a time series from such systems to a complex network. The natural approach is to calculate the recurrence matrix and interpret such as the adjacency matrix of an associated complex network, called recurrence network. Using complex network measures, such as transitivity coefficient, we demonstrate that this approach is very efficient for identifying qualitative transitions in observational data, e.g., when analyzing paleoclimate regime transitions. Second, we demonstrate the use of directed spatial networks constructed from spatio-temporal measurements of such systems that can be derived from the synchronized-in-time occurrence of extreme events in different spatial regions. Although there are many possibilities to investigate such spatial networks, we present here the new measure of network divergence and how it can be used to develop a prediction scheme of extreme rainfall events.

Nonlinear time-series analysis revisited

In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data-typically univariate-via dynamical systems theory. Based on the concept of state-space reconstruction, this set of methods allows us to compute characteristic quantities such as Lyapunov exponents and fractal dimensions, to predict the future course of the time series, and even to reconstruct the equations of motion in some cases. In practice, however, there are a number of issues that restrict the power of this approach: whether the signal accurately and thoroughly samples the dynamics, for instance, and whether it contains noise. Moreover, the numerical algorithms that we use to instantiate these ideas are not perfect; they involve approximations, scale parameters, and finite-precision arithmetic, among other things. Even so, nonlinear time-series analysis has been used to great advantage on thousands of real and synthetic data sets from a wide variety of systems ranging from roulette wheels to lasers to the human heart. Even in cases where the data do not meet the mathematical or algorithmic requirements to assure full topological conjugacy, the results of nonlinear time-series analysis can be helpful in understanding, characterizing, and predicting dynamical systems.

Nonlinear feature extraction for objective classification of complex auditory brainstem responses to diotic perceptually critical consonant-vowel syllables

OBJECTIVE

To examine if nonlinear feature extraction method yields appropriate results in complex brainstem response classification of three different consonant vowels diotically presented in normal Persian speaking adults.

METHODS

Speech-evoked auditory brainstem responses were obtained in 27 normal hearing young adults by using G.tec EEG recording system. 170ms synthetic consonant-vowel stimuli /ba/, /da/, /ga/ were presented binaurally and the recurrence quantification analysis was performed on the responses. The recurrence time of second type was proposed as a suitable feature. ANOVA was also used for testing the significance of extracted feature. Post-comparison statistical method was used for showing which means are significantly different from each other.

RESULTS

Dimension embedding and state space reconstruction were helpful for visualizing nonlinearity in auditory system. The proposed feature was successful in the objective classification of responses in window time 20.1-35.3ms, which belonged to formant transition period of stimuli. Also the p value behavior of recurrence time of second type feature as a discriminant feature was close to the nature of the response that includes transient and sustained parts. On the other hand, the /ba/ and /ga/ classification period was wider than the others.

CONCLUSION

The extracted feature shown in this paper is helpful for the objective of distinguishing individuals with auditory processing disorders in the structurally similar voices. On the other hand, differing nonlinear feature is meaningful in a special region of response, equal to formant transition period, and this feature is related to the state space changes of brainstem response. It can be assumed that more information is within this region of signal and it is a sign of processing role of brainstem. The state changes of system are dependent on input stimuli, so the existence of top down feedback from cortex to brainstem forces the system to act differently.

Adaptive correlation dimension method for analysing heart rate variability during the menstrual cycle

Correlation dimension (CD) is used for analysing the chaotic behaviour of the nonlinear heart rate variability (HRV) time series. In CD, the autocorrelation function is used to calculate the time delay. However, it does not provide optimum values of time delays, which leads to an inaccurate estimation of the HRV between phases of the menstrual cycle. Thus, an adaptive CD method is presented here to calculate the optimum value of the time delay based upon the information content in the HRV signal. In the proposed method, the first step is to divide the HRV signal into overlapping windows. Afterwards, the time delay is calculated for each window based on the features of the signal. This procedure of finding the optimum time delay for each window is known as adaptive autocorrelation. Then, the CD for each window is calculated using optimum time delays. Finally, adaptive CD is calculated by averaging the CD of all windows. The proposed method is applied on two data sets: (i) the standard Physionet dataset and (ii) the dataset acquired using BIOPAC(®)MP150. The results show that the proposed method can accurately differentiate between normal and diseased subjects. Further, the results prove that the proposed method is more accurate in detecting HRV variations during the menstrual cycles of 74 young women in lying and standing postures. Three statistical parameters are used to find the effectiveness of adaptive autocorrelation in calculating time delays. The comparative analysis validates the superiority of the proposed method over detrended fluctuation analyses and conventional CD.

The effects of movement speed on kinematic variability and dynamic stability of the trunk in healthy individuals and low back pain patients

BACKGROUND

Comparison of the kinematic variability and dynamic stability of the trunk between healthy and low back pain patient groups can contribute to gaining valuable information about the movement patterns and neuromotor strategies involved in various movement tasks.

METHODS

Fourteen chronic low back pain patients with mild symptoms and twelve healthy male volunteers performed repeated trunk flexion-extension movements in the sagittal plane at three different speeds: 20 cycles/min, self-selected, and 40 cycles/min. Mean standard deviations, coefficient of variation and variance ratio as variability measures; maximum finite-time Lyapunov exponents and maximum Floquet multipliers as stability measures were computed from trunk kinematics.

FINDINGS

Higher speed significantly reduced the kinematic variability, while it increased short-term Lyapunov exponents. Long-term Lyapunov exponents were higher at self-selected speed and lower in low back pain patients as compared to control volunteers. Floquet multipliers were larger at self-selected speed and during higher pace trunk movements.

INTERPRETATION

Our findings suggest that slower pace flexion-extension trunk movements are associated with more motor variation as well as local and orbital stability, implying less potential risk of injury for the trunk. Individuals with and without low back pain consistently recruited a closed-loop control strategy towards achieving trunk stability. Chronic low back pain patients exhibited more stable trunk movements over long-term periods, indicating probable temporary pain relief functional adaption strategies. These results may be used towards the development of more effective personalized rehabilitation strategies and quantitative spinal analysis tools for low back pain detection, diagnosis and treatment, as well as improvement of workspace and occupational settings.

Long-term scalp epileptic EEG quantification with GMA dynamics

The paper concerns the problem of automatic seizure detection based on scalp EEG and proposes to employ the generalized measure of association (GMA) to quantify the statistical dependencies and infer the dynamical interactions of brain regions with the focus area. The experimental results with clinical recordings show that the estimated GMA values changes dramatically before and during epileptic seizures reflecting the dynamic coupling and decoupling between brain regions, which can be an useful measure to quantify epileptic EEG signals.

Dimensionality reduction and dynamical filtering: Stimulated Brillouin scattering in optical fibers

Stimulated Brillouin scattering (SBS) is a noise-driven nonlinear interaction between acoustical and optical waves. In optical fibers, SBS can be observed at relatively low optical powers and can severely limit signal transmission. Although SBS is initiated by high dimensional noise, it also exhibits many of the hallmarks of a complex nonlinear dynamical system. We report here a comprehensive experimental and numerical study of the fluctuations in the reflected Stokes wave produced by SBS in optical fibers. Using time series analysis, we demonstrate a reduction of dimensionality and dynamical filtering of the Stokes wave. We begin with a careful comparison of the measured average transmitted and reflected intensities from below the SBS threshold to saturation of the transmitted power. Initially the power spectra and correlation functions of the time series of the reflected wave fluctuations at the SBS threshold and above are measured and simulated. Much greater dynamical insight is provided when we study the scaling behavior of the intensity fluctuations using Hurst exponents and detrended fluctuation analysis for time scales extending over six orders of magnitude. At the highest input powers, we notice the emergence of three distinct dynamical scaling regimes: persistent, Brownian, and antipersistent. Next, we explore the Hilbert phase fluctuations of the intensity time series and amplitude-phase coupling. Finally, time-delay embedding techniques reveal a gradual reduction in dimensionality of the spatiotemporal dynamics as the laser input is increased toward saturation of the transmitted power. Through all of these techniques, we find a transition from noisier to smoother dynamics with increasing input power. We find excellent agreement between our experimental measurements and simulations.

Nonlinear parameters of surface EMG in schizophrenia patients depend on kind of antipsychotic therapy

We compared a set of surface EMG (sEMG) parameters in several groups of schizophrenia (SZ, n = 74) patients and healthy controls (n = 11) and coupled them with the clinical data. sEMG records were quantified with spectral, mutual information (MI) based and recurrence quantification analysis (RQA) parameters, and with approximate and sample entropies (ApEn and SampEn). Psychotic deterioration was estimated with Positive and Negative Syndrome Scale (PANSS) and with the positive subscale of PANSS. Neuroleptic-induced parkinsonism (NIP) motor symptoms were estimated with Simpson-Angus Scale (SAS). Dyskinesia was measured with Abnormal Involuntary Movement Scale (AIMS). We found that there was no difference in values of sEMG parameters between healthy controls and drug-naïve SZ patients. The most specific group was formed of SZ patients who were administered both typical and atypical antipsychotics (AP). Their sEMG parameters were significantly different from those of SZ patients taking either typical or atypical AP or taking no AP. This may represent a kind of synergistic effect of these two classes of AP. For the clinical data we found that PANSS, SAS, and AIMS were not correlated to any of the sEMG parameters.

CONCLUSION

with nonlinear parameters of sEMG it is possible to reveal NIP in SZ patients, and it may help to discriminate between different clinical groups of SZ patients. Combined typical and atypical AP therapy has stronger effect on sEMG than a therapy with AP of only one class.

The relationship between node degree and dissipation rate in networks of diffusively coupled oscillators and its significance for pancreatic beta cells

Self-sustained oscillatory dynamics is a motion along a stable limit cycle in the phase space, and it arises in a wide variety of mechanical, electrical, and biological systems. Typically, oscillations are due to a balance between energy dissipation and generation. Their stability depends on the properties of the attractor, in particular, its dissipative characteristics, which in turn determine the flexibility of a given dynamical system. In a network of oscillators, the coupling additionally contributes to the dissipation, and hence affects the robustness of the oscillatory solution. Here, we therefore investigate how a heterogeneous network structure affects the dissipation rate of individual oscillators. First, we show that in a network of diffusively coupled oscillators, the dissipation is a linearly decreasing function of the node degree, and we demonstrate this numerically by calculating the average divergence of coupled Hopf oscillators. Subsequently, we use recordings of intracellular calcium dynamics in pancreatic beta cells in mouse acute tissue slices and the corresponding functional connectivity networks for an experimental verification of the presented theory. We use methods of nonlinear time series analysis to reconstruct the phase space and calculate the sum of Lyapunov exponents. Our analysis reveals a clear tendency of cells with a higher degree, that is, more interconnected cells, having more negative values of divergence, thus confirming our theoretical predictions. We discuss these findings in the context of energetic aspects of signaling in beta cells and potential risks for pathological changes in the tissue.