Nonlinear Phase Coupling Research Articles

Recognition of regions of stroke injury using multi-modal frequency features of electroencephalogram.

Nowadays, increasingly studies are attempting to analyze strokes in advance. The identification of brain damage areas is essential for stroke rehabilitation. We proposed Electroencephalogram (EEG) multi-modal frequency features to classify the regions of stroke injury. The EEG signals were obtained from stroke patients and healthy subjects, who were divided into right-sided brain injury group, left-sided brain injury group, bilateral brain injury group, and healthy controls. First, the wavelet packet transform was used to perform a time-frequency analysis of the EEG signal and extracted a set of features (denoted as WPT features). Then, to explore the nonlinear phase coupling information of the EEG signal, phase-locked values (PLV) and partial directed correlations (PDC) were extracted from the brain network, and the brain network produced a second set of features noted as functional connectivity (FC) features. Furthermore, we fused the extracted multiple features and used the resnet50 convolutional neural network to classify the fused multi-modal (WPT + FC) features. The classification accuracy of our proposed methods was up to 99.75%. The proposed multi-modal frequency features can be used as a potential indicator to distinguish regions of brain injury in stroke patients, and are potentially useful for the optimization of decoding algorithms for brain-computer interfaces.

Combining enhanced spectral resolution of EMG and a deep learning approach for knee pathology diagnosis.

Knee osteoarthritis (OA) is a prevalent, debilitating joint condition primarily affecting the elderly. This investigation aims to develop an electromyography (EMG)-based method for diagnosing knee pathologies. EMG signals of the muscles surrounding the knee joint were examined and recorded. The principal components of the proposed method were preprocessing, high-order spectral analysis (HOSA), and diagnosis/recognition through deep learning. EMG signals from individuals with normal and OA knees while walking were extracted from a publicly available database. This examination focused on the quadriceps femoris, the medial gastrocnemius, the rectus femoris, the semitendinosus, and the vastus medialis. Filtration and rectification were utilized beforehand to eradicate noise and smooth EMG signals. Signals' higher-order spectra were analyzed with HOSA to obtain information about nonlinear interactions and phase coupling. Initially, the bicoherence representation of EMG signals was devised. The resulting images were fed into a deep-learning system for identification and analysis. A deep learning algorithm using adapted ResNet101 CNN model examined the images to determine whether the EMG signals were conventional or indicative of knee osteoarthritis. The validated test results demonstrated high accuracy and robust metrics, indicating that the proposed method is effective. The medial gastrocnemius (MG) muscle was able to distinguish Knee osteoarthritis (KOA) patients from normal with 96.3±1.7% accuracy and 0.994±0.008 AUC. MG has the highest prediction accuracy of KOA and can be used as the muscle of interest in future analysis. Despite the proposed method's superiority, some limitations still require special consideration and will be addressed in future research.

An experimental study on nonlinear wave dynamics for freak waves over an uneven bottom

The effect of the non-uniform bathymetry on the nonlinear wave dynamics for the freak wave is investigated experimentally, with emphasis on the interrelations between different nonlinear behaviors resulting from various geometric parameters and spectral analysis. Both the frequency modulation and the nonlinear phase coupling can be provoked by the decreasing water depth and weakened after the top peak of the bar, the nonlinear exhibition for transferring energy to high-frequency contents over shoal supports that frequency modulation can reflect nonlinear phase coupling well. The consistent change of the Hilbert energy spectrum and the bicoherence shows that the main nonlinear interaction in the process of wave propagation in shallowing water is quadratic nonlinearity. In addition, the geometric study is conducted to investigate the effect of the water depth on the parametric variations, the research results show that the mean asymmetry and kurtosis change abruptly when the wave approaches the top peak of the bar. As the wave propagates along the water flume, freak waves can be generated at various locations, however, they appear more frequently as waves propagate close to the shallowest water depth, and the maximum probability of occurrence for a freak wave can be up to about 1%.

Experimental study on the effect of an oyster reef on the nonlinear characteristics of irregular waves

As a “marine ecological engineer”, the oyster reefs not only perform important ecological functions, but also reduce the damage caused by waves to protective structures such as seawalls. However, oyster reefs in shallow water change the nonlinear characteristics of waves and affect sediment transport and coastal evolution. Based on Fourier spectrum and analysis of Wavelet Transform, the influence of artificial bag oyster reefs on the energy and nonlinear phase coupling of irregular waves are studied through physical experiment. The results show that oyster reefs have a substantial effect on the energy of primary harmonic, which transfer to higher harmonics through triad interactions, and a considerable reduction in primary harmonic energy and an increase in higher harmonics energy are reflected in the energy spectra. The transmission spectrum behind the oyster reefs shows three peaks at primary, secondary and third harmonics. The bicoherence spectrum indicates that the peaks at secondary and third harmonics mainly result from the self-coupling of the primary harmonics and phase coupling between the primary and secondary harmonics respectively. As the water depth increases, the degree of nonlinear coupling between wave components decreases, which leads to the energy of wave components at different frequencies increases. With increasing top width, the length of the shoaling region increases, and the growth of triad nonlinear interactions are observed in wavelet-based bicoherence spectra, resulting in the spectral peak energy decreasing while the secondary harmonics energy increasing in the spectrum. Finally, the potential application of an ecological system composed by “oyster reefs + mangroves” is discussed. As the effect of water depth on wave energy is much greater than that of top width, in artificial oyster reef construction, it is recommended that keep the oyster reefs non-submerged in terms of wave dissipation. Further studies should take the dynamic growth effect of oyster reefs into account.

Decoding Adaptive Visuomotor Behavior Mediated by Non-linear Phase Coupling in Macaque Area MT.

The idea that a flexible behavior relies on synchronous neural activity within intra- and inter-associated cortical areas has been a matter of intense research in human and animal neuroscience. The neurophysiological mechanisms underlying this behavioral correlate of the synchronous activity are still unknown. It has been suggested that the strength of neural synchrony at the level of population is an important neural code to guide an efficient transformation of the sensory input into the behavioral action. In this study, we have examined the non-linear synchronization between neural ensembles in area MT of the macaque visual cortex by employing a non-linear cross-frequency coupling technique, namely bicoherence. We trained a macaque monkey to detect a brief change in the cued stimulus during a visuomotor detection task. The results show that the non-linear phase synchronization in the high-gamma frequency band (100–250 Hz) predicts the animal’s reaction time. The strength of non-linear phase synchronization is selective to the target stimulus location. In addition, the non-linearity characteristics of neural synchronization are selectively modulated when the monkey covertly attends to the stimulus inside the neuron’s receptive field. This additional evidence indicates that non-linear neuronal synchronization may be affected by a cognitive function like spatial attention. Our neural and behavioral observations reflect that two crucial processes may be involved in processing of visuomotor information in area MT: (I) a non-linear cortical process (measured by the bicoherence) and (II) a linear process (measured by the spectral power).

Experimental study of hypersonic boundary layer transition on a flat plate delta wing

The boundary layer transition on a flat plate delta wing was investigated in the Mach 6 quiet wind tunnel via global temperature and wall pressure measurements as well as flow visualization. The results show that the boundary layer transition on side line is earlier than that on center line, and larger angle of attack promotes the boundary layer transition. As the Reynolds number increases, the transition position of boundary layer moves upstream. The hot streaks on the center line of delta wing at 0° angle of attack which are symmetrically distributed with respect to the center line at 10° angle of attack are suspected to be arised from the vortical flow rather than the boundary layer transition. High frequency disturbances occurring nonlinear phase coupling transfer the energy to low frequency structures, and finally the low frequency large scale structures induce to boundary layer transition. The intensity of nonlinear interaction prior to boundary layer transition is stronger than that in turbulent boundary layer. In addition, the unstable region of disturbance waves depends on the Reynolds number.

Nonlinear phase coupling functions: a numerical study.

Phase reduction is a general tool widely used to describe forced and interacting self-sustained oscillators. Here, we explore the phase coupling functions beyond the usual first-order approximation in the strength of the force. Taking the periodically forced Stuart-Landau oscillator as the paradigmatic model, we determine and numerically analyse the coupling functions up to the fourth order in the force strength. We show that the found nonlinear phase coupling functions can be used for predicting synchronization regions of the forced oscillator. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

The HEURECA method: Tracking multiple phase coupling dynamics on a single trial basis

BackgroundAlthough acquisition techniques have improved tremendously, the neuroscientific understanding of complex cognitive phenomena is still incomplete. One of the reasons for this shortcoming may be the lack of sophisticated signal processing methods. Complex cognitive phenomena usually involve various mental subprocesses whose temporal occurrence varies from trial to trial. Mostly, these mental subprocesses require large-scale integration processes between multiple brain areas that are most likely mediated by complex, non-linear phase coupling mechanisms. Consequently, a spatiotemporal analysis of complex, multivariate phase synchronization patterns on a single trial basis is necessary. New methodThis paper introduces the HEURECA method (How to Evaluate and Uncover Recurring EEG Coupling Arrangements) that enables the dynamic detection of distinguishable multivariate functional connectivity states in the electroencephalogram. HEURECA adaptively divides a trial into segments of quasi-stable phase coupling topographies and assigns similar topographies to the same synchrostate cluster. ResultsHEURECA is evaluated by means of simulated data. The results show that it reliably reconstructs a time series of recurring phase coupling topographies and successfully gathers them into clusters of interpretable neural synchrostates. The advantages and unique features of HEURECA are further illustrated by investigating the popular complex cognitive phenomenon insight. Comparison with existing methodsUnlike existing methods, HEURECA detects complex phase relationships between more than two signals and is applicable to single trials. ConclusionsSince HEURECA is applicable to all kinds of circular data, it not only provides new insights into insight, but also into a variety of other phenomena in neuroscience, physics or other scientific fields.

Effects of recess depth and opening diameter on pressure measurement by recess mounted transducers in a hypersonic boundary layer

Experimental measurements of pressure fluctuations in a hypersonic boundary layer were conducted based on recess mounted transducers and the effects of recess depth and opening diameter on fluctuating pressure characteristics were studied. The results showed that as the recess depth increased, the bulk of counter flow in the cavity enlarged with the decreased energy of large scale structures, and more small scale structures with relatively high frequency were generated which contributed to the multiscale structures with broadband frequency spectrum. Similarly, as the opening diameter increased, the low-frequency large scale structures inside the cavity had larger energy due to the shear flow entering the cavity having more mass and carrying larger energy, and the small scale structures with high frequency exhibited stronger dissipation intensity. The symmetric and stable flow filed was more likely to cause the cavity resonance, and the asymmetry and instability of the flow field for smaller recess depth as well as larger opening diameter could inhibit the cavity resonance. Compared to surface mounted, nonlinear phase coupling occurred between the flow structures caused by recess mounting which transfered the energy from high-frequency structures to low-frequency structures. On the whole, smaller recess depth and larger opening diameter are optimized in the hypersonic flight test on the premise of pressure sensors not destroyed by the harsh aerothermodynamic environment.

Nonlinear Connectivity in the Human Stretch Reflex Assessed by Cross-Frequency Phase Coupling.

Communication between neuronal populations is facilitated by synchronization of their oscillatory activity. Although nonlinearity has been observed in the sensorimotor system, its nonlinear connectivity has not been widely investigated yet. This study investigates nonlinear connectivity during the human stretch reflex based on neuronal synchronization. Healthy participants generated isotonic wrist flexion while receiving a periodic mechanical perturbation to the wrist. Using a novel cross-frequency phase coupling metric, we estimate directional nonlinear connectivity, including time delay, from the perturbation to brain and to muscle, as well as from brain to muscle. Nonlinear phase coupling is significantly stronger from the perturbation to the muscle than to the brain, with a shorter time delay. The time delay from the perturbation to the muscle is 33 ms, similar to the reported latency of the spinal stretch reflex at the wrist. Source localization of nonlinear phase coupling from the brain to the muscle suggests activity originating from the motor cortex, although its effect on the stretch reflex is weak. As such nonlinear phase coupling between the perturbation and muscle activity is dominated by the spinal reflex loop. This study provides new evidence of nonlinear neuronal synchronization in the stretch reflex at the wrist joint with respect to spinal and transcortical loops.

Laboratory study of the nonlinear transformation of irregular waves over a mild slope

This paper considers the nonlinear transformation of irregular waves propagating over a mild slope (1:40). Two cases of irregular waves, which are mechanically generated based on JONSWAP spectra, are used for this purpose. The results indicate that the wave heights obey the Rayleigh distribution at the offshore location; however, in the shoaling region, the heights of the largest waves are underestimated by the theoretical distributions. In the surf zone, the wave heights can be approximated by the composite Weibull distribution. In addition, the nonlinear phase coupling within the irregular waves is investigated by the wavelet-based bicoherence. The bicoherence spectra reflect that the number of frequency modes participating in the phase coupling increases with the decreasing water depth, as does the degree of phase coupling. After the incipient breaking, even though the degree of phase coupling decreases, a great number of higher harmonic wave modes are also involved in nonlinear interactions. Moreover, the summed bicoherence indicates that the frequency mode related to the strongest local nonlinear interactions shifts to higher harmonics with the decreasing water depth.

PHASE SYNCHRONIZATION OF NEURONAL NOISE IN MOUSE HIPPOCAMPAL EPILEPTIFORM DYNAMICS

Organized brain activity is the result of dynamical, segregated neuronal signals that may be used to investigate synchronization effects using sophisticated neuroengineering techniques. Phase synchrony analysis, in particular, has emerged as a promising methodology to study transient and frequency-specific coupling effects across multi-site signals. In this study, we investigated phase synchronization in intracellular recordings of interictal and ictal epileptiform events recorded from pairs of cells in the whole (intact) mouse hippocampus. In particular, we focused our analysis on the background noise-like activity (NLA), previously reported to exhibit complex neurodynamical properties. Our results show evidence for increased linear and nonlinear phase coupling in NLA across three frequency bands [theta (4-10 Hz), beta (12-30 Hz) and gamma (30-80 Hz)] in the ictal compared to interictal state dynamics. We also present qualitative and statistical evidence for increased phase synchronization in the theta, beta and gamma frequency bands from paired recordings of ictal NLA. Overall, our results validate the use of background NLA in the neurodynamical study of epileptiform transitions and suggest that what is considered "neuronal noise" is amenable to synchronization effects in the spatiotemporal domain.

Application of Bipectrum in Mechanical Fault Diagnosis

Bispectrum produced by third order cumulant contains the asymmetric and nonlinear information of signal, which can be used to describe the nonlinear phase coupling, especially the quadratic phase coupling, has been widely applied in fault diagnosis. The features of fault signals and normal signals are fetched by 2-D wavelet in different directions, then these features are used to diagnose fault. The experiment shows that the method can achieve satisfactory result.

Laboratory Study of Unidirectional Focusing Waves in Intermediate Depth Water

The results of laboratory measurements of large focusing wave groups, which were generated using the New Wave theory, are presented. The influences of both the steepness and frequency bandwidth on focused wave characteristics were examined. The influence of frequency bandwidth on focused wave groups with small and moderate steepness was very small. However, for cases with the large steepness, the nonlinearity increased with increasing bandwidth frequency and widened free-wave regimes are identified for those cases with large steepness at the focal location. The underlying nonlinear phase coupling of focused waves was examined using wavelet-based bicoherence and biphase, which can detect nonlinear phase coupling in a short time series. For wave groups with large initial steepness, as wave groups approached the focal location, the values of bicoherence between primary waves and its higher harmonics progressively increased to 1 and the corresponding biphase was gradually close to zero, suggesting that an extreme wave event can be produced by considering Stokes-like nonlinearity to very high-order. Furthermore, the fast change of bicoherence of focused wave groups indicates that the nonlinear energy transfer within focusing waves is faster than that of nonfocusing wave trains.

Experimental study of wave–wave nonlinear interactions using the wavelet-based bicoherence

The wavelet-based bicoherence, which is a new and powerful tool in the analysis of nonlinear phase coupling, is used to study the nonlinear wave–wave interactions of breaking and non-breaking gravity waves propagating over a sill. Two cases of mechanically generated random waves based on J onswap spectra are used for this purpose. Values of relative depth, k p h ( k p is the wave number of the spectral peak and h is the water depth) for this study range between 0.38 and 1.22. The variations of wavelet-based total bicoherence for the test cases indicate that the degree of quadratic phase coupling increases in the shoaling region consistent with a wave profile that is pitched shoreward, relative to a vertical axis as seen in the experiments, but decreases in the de-shoaling region. For the non-breaking case, the degree of quadratic phase coupling continues to increase until waves reach the top of the sill. Breaking waves, however, achieve their highest level of quadratic phase coupling immediately before incipient breaking and the degree of phase coupling decreases sharply following breaking. In addition the wavelet-based bicoherence spectra provide evidence of the harmonics' growth which is reflected in the energy spectra. The bicoherence spectra also show that quadratic phase coupling between modes within the peak frequency as well as between modes of the peak frequency and its higher harmonics are dominant in the shoaling region, even though there are relatively high levels of quadratic phase coupling occurring between other frequencies. Furthermore, using the temporal resolution property of the wavelet-based bicoherence, we find that the quadratic wave interactions occur more readily during segments of time with large change of wave amplitude, rather than those segments having large wave amplitudes, but small gradients in amplitude.

Nonlinear interactions in the visual system: a steady-state VEP study

To study the interaction between different receptive fields in human visual processing, the present study investigated the steady-state evoked potentials (ss-VEPs) by two light emitting diodes (LEDs) lit at the different temporal frequencies, which were presented separately to each hemivisual field of the subjects. Two LEDs set in front of the subject were energized at different temporal frequencies of combinations of 7, 9, 11, and 13 Hz. The subject was asked to look at a fixation point at the midpoint. Nineteen EEGs were recorded and the data were averaged 80–100 times triggered at the peak of a light intensity for each quartile range of phase lag. The phase dependency was studied by comparing steady-state visual evoked potentials (ss-VEPs) and also by using higher-order spectra (HOS). The interactions between background EEGs and ss-VEPs were also investigated. The power spectra of ss-VEPs exhibited peaks at the frequency other than those of stimuli. HOS analysis showed that nonlinear phase coupling between the peak frequencies of ss-VEPs were partially detected. Frequencies of the visual stimuli were suspected to reflect onto the bilateral visual area. The changes in the ss-VEPs triggered by the peak of stimuli were affected by the phase lag between bilateral stimuli. Our results are suggestive of some nonlinear interactions in the visual processing over the different areas.

Observations of nearshore infragravity waves: Seaward and shoreward propagating components

The variation of seaward and shoreward infragravity energy fluxes across the shoaling and surf zones of a gently sloping sandy beach is estimated from field observations and related to forcing by groups of sea and swell, dissipation, and shoreline reflection. Data from collocated pressure and velocity sensors deployed between 1 and 6 m water depth are combined, using the assumption of cross‐shore propagation, to decompose the infragravity wave field into shoreward and seaward propagating components. Seaward of the surf zone, shoreward propagating infragravity waves are amplified by nonlinear interactions with groups of sea and swell, and the shoreward infragravity energy flux increases in the onshore direction. In the surf zone, nonlinear phase coupling between infragravity waves and groups of sea and swell decreases, as does the shoreward infragravity energy flux, consistent with the cessation of nonlinear forcing and the increased importance of infragravity wave dissipation. Seaward propagating infragravity waves are not phase coupled to incident wave groups, and their energy levels suggest strong infragravity wave reflection near the shoreline. The cross‐shore variation of the seaward energy flux is weaker than that of the shoreward flux, resulting in cross‐shore variation of the squared infragravity reflection coefficient (ratio of seaward to shoreward energy flux) between about 0.4 and 1.5.

Phase-coupling of theta–gamma EEG rhythms during short-term memory processing

Because of the importance of oscillations as a general phenomenon of neuronal activity the use of EEG spectral analysis is among the most important approaches for studying human information processing. Usually, oscillations at different frequencies occur simultaneously during information processing. Thus, the question for synchronisation of different frequencies by phase coupling and its possible functional significance is of primary importance. An answer may be given by bispectral analysis. Estimation of the (cross-) bispectrum allows to identify synchronised frequencies and possibly, the existence of non-linear phase coupling of different oscillators. Previous studies have demonstrated the simultaneous occurrence of slow (4–7 Hz) and fast (20–30 Hz) oscillations at frontal and prefrontal electrode positions during memory processing. However, interrelations between these rhythms have not been investigated up to now. In order to test short-term memory, the Sternberg task with random figures and number words was carried out on 10 female subjects. During the task EEG was recorded. Power and bispectral analyses from frontal, prefrontal and frontopolar regions were performed off-line. Increased power was found in both the theta and the gamma bands. Strong phase-coupling between theta at Fz and gamma at F3 and at Fp1, respectively, was shown for memorising number words by means of cross-bicoherence. A possible reason for this is an amplitude modulation of gamma frequencies by slow oscillations. The correspondent coherence analysis between the envelope of gamma frequencies at Fp1 and the raw EEG at Fz supports this presumption. This finding is interpreted as an EEG aspect of the functional linking between the prefrontal areas and the G.cinguli (as part of the limbic system), which are both extremely important for memory functions.

In search of zonal flows using cross-bispectrum analysis in the boundary plasma of the Hefei Tokamak-7

Langmuir probes have been used to measure the electrostatic Reynolds stress and the floating potential fluctuation in the boundary plasma of the Hefei Tokamak-7 (HT-7) [J. Li, B. N. Wan, and J. S. Mao, Plasma Phys. Controlled Fusion 42, 135 (2000)]. The cross bispectrum of 〈ṼrṼθφ̃f〉 indicates the existence of difference-frequency nonlinear phase coupling and the generation of fluctuations near the geodesic acoustic mode frequency. The inverse cascade process might be linked to the generation of zonal flows by small-scale electrostatic drift-wave turbulence.

EEG Frequency and Phase Coupling during Human Information Processing

Neuronal activity during information processing is represented by oscillations within local or widespread neuronal networks. These oscillations may be recorded by the EEG (electroencephalogram). The oscillatory interaction between neuronal ensembles may be at one single frequency or at different frequencies due to non-linear coupling. The investigation of momentary coherence and phase enables the examination of synchronized oscillatory network activity during fast-changing cognitive processes. On this basis information transfer from occipital areas towards frontal areas could be described during processing of visual presented words. Non-linear phase coupling between oscillations with different frequencies during memory processing was detected by means of cross-bicoherence.