Phase Synchronization Research Articles

Real-time measurements of breathing dissipative soliton pairs in mode-locked fiber lasers

The emergence of breathing solitons, as well as the breathing soliton molecules undergoing periodic evolution in peak power and spectral width has attracted growing research attentions in dissipative systems. Beyond the intense pulse interactions within tightly-bound states with picoseconds interval, the long-range interplay between pulses separated by nanosecond-scale starts to be investigated in recent years, thus filling the long-standing academic gap between the bound solitons and independent multiple pulses. In this work, we report on the real-time observations of breathing dissipative soliton pairs with nanoseconds’ separations in a fiber laser operating under the threshold of stationary mode locking. Compared with conventional soliton counterpart, here the breathing soliton pair exhibit even more fascinating inter-pulse nonlinear dynamics due to the intriguing self-excited periodic evolutions. The shot-to-shot measurements of pulse intensity profiles, associated with dispersive Fourier transform clearly uncover not only the different breathing phase synchronization and pulse separations among different pulses but also the hysteresis behaviors of the breathing ratio by continuously varying the laser parameters. Moreover, we observed various transient stages in this unstable lasing regime, including the transition between stable single soliton and breathing soliton pair, as well as their long-range breather interaction. These results reveal the breathing multi-pulse state and the instantaneous non-equilibrium dynamics involving the breather pairs, enriching the framework of breathing solitons and opening a novel possibility to explore the internal motions of breathing soliton complex in nonlinear systems.

Fixed‐time Synchronization of Stochastic Kuramoto‐Oscillator Networks With Switching Topology Under Dynamic Event‐triggered Scheme

AbstractThis paper proposes a dynamic event‐triggered fixed‐time control scheme for the phase synchronization of Kuramoto networks with switching topology and stochastic coupling noise. To deal with the problems of switching topology and stochastic coupling noise, a multilayered control structure with a specially designed noise reduction layer is developed. The effectiveness is proved based on stochastic differential theory. To save communication resources and reduce control frequency, a dynamic event‐triggered mechanism is proposed. By introducing a dynamic variable into the triggering condition, the triggered instants are further reduced compared to the traditional static event‐triggered method. The synchronizing criteria and parameter conditions are established with stochastic Lyapunov stability theory. The analysis of Zeno behavior is also given. Finally, numerical simulation experiments are conducted to demonstrate the effectiveness of the proposed dynamic event‐triggered control scheme.

Previous motor task performance impacts phase-based EEG resting-state connectivity states

Abstract The resting human brain cycles through distinct states that can be analyzed using microstate analysis and electroencephalography (EEG) data. This approach classifies multichannel EEG data into spontaneously interchanging microstates based on topographic features. These microstates may be valuable biomarkers in neurodegenerative diseases since they reflect the resting brain’s state. However, microstates do not provide information about the active neural networks during the resting state. This article presents an alternative and complementary method for analyzing resting-state EEG data and demonstrates its reproducibility and reliability. This method considers cerebral connectivity states defined by phase synchronization and measured using the corrected imaginary phase-locking value (ciPLV) based on source-reconstructed EEG recordings. We analyzed resting-state EEG data from young, healthy participants acquired on five consecutive days before and after a motor task. We show that our data reproduce microstates previously reported. Further, we reveal four stable topographic patterns over the multiple recording sessions in the source connectivity space. While the classical microstates were unaffected by a preceding motor task, the connectivity states were altered, reflecting the suppression of frontal activity in the post-movement resting state.

Effects of uncommon non-isochronicities on remote synchronization

Remote synchronization (RS) is referred to as the weak synchronization between indirectly coupled nodes (among leaf nodes) while asynchronous between the directed coupled nodes (i.e., hub and leaf nodes). The underlying mechanisms are related to (i) coupling terms indirectly connecting two nearly identical oscillators while having a much different mediator in between, (ii) non-isochronicity of the oscillators. Here we show the effects of uncommon non-isochronicity values of oscillators on the occurrence of RS. In addition, we show clear difference of using either the first order phase approximations of the Stuart–Landau oscillators or Kuramoto–Sakaguchi (KS) models to study RS. By both theoretical and numerical analysis, we show that the critical coupling for synchronization between the directly connected nodes is inversely proportional to the difference value of non-isochronicity. On the contrary, the critical coupling for RS between indirectly connected leaf nodes is determined by the sum of non-isochronicity. In addition, RS may experience fading out after the first appearance when the coupling is progressively increased, which is indeed time delayed phase synchronization.

Inter-brain desynchronization in social interaction: a consequence of subjective involvement?

Hyperscanning approaches to human neuroscience aim to uncover the neural mechanisms of social interaction. They have been largely guided by the expectation that increased levels of engagement between two persons will be supported by higher levels of inter-brain synchrony (IBS). A common approach to measuring IBS is phase synchrony in the context of EEG hyperscanning. Yet the growing number of experimental findings does not yield a straightforward interpretation, which has prompted critical reflections about the field's theoretical and methodological principles. In this perspective piece, we make a conceptual contribution to this debate by considering the role of a possibly overlooked effect of inter-brain desynchronization (IBD), as for example measured by decreased phase synchrony. A principled reason to expect this role comes from the recent proposal of irruption theory, which operationalizes the efficacy of a person's subjective involvement in behavior generation in terms of increased neural entropy. Accordingly, IBD is predicted to increase with one or more participant's socially motivated subjective involvement in interaction, because of the associated increase in their neural entropy. Additionally, the relative prominence of IBD compared to IBS is expected to vary in time, as well as across frequency bands, depending on the extent that subjective involvement is elicited by the task and/or desired by the person. If irruption theory is on the right track, it could thereby help to explain the notable variability of IBS in social interaction in terms of a countertendency from another factor: IBD due to subjective involvement.

Unsupervised ensembling of multiple software sensors with phase synchronization: a robust approach for electrocardiogram-derived respiration

Objective. We aimed to fuse the outputs of different electrocardiogram-derived respiration (EDR) algorithms to create one higher quality EDR signal. Methods. We viewed each EDR algorithm as a software sensor that recorded breathing activity from a different vantage point, identified high-quality software sensors based on the respiratory signal quality index, aligned the highest-quality EDRs with a phase synchronization technique based on the graph connection Laplacian, and finally fused those aligned, high-quality EDRs. We refer to the output as the sync-ensembled EDR signal. The proposed algorithm was evaluated on two large-scale databases of whole-night polysomnograms. We evaluated the performance of the proposed algorithm using three respiratory signals recorded from different hardware sensors, and compared it with other existing EDR algorithms. A sensitivity analysis was carried out for a total of five cases: fusion by taking the mean of EDR signals, and the four cases of EDR signal alignment without and with synchronization and without and with signal quality selection. Results. The sync-ensembled EDR algorithm outperforms existing EDR algorithms when evaluated by the synchronized correlation ( γ -score), optimal transport (OT) distance, and estimated average respiratory rate score, all with statistical significance. The sensitivity analysis shows that the signal quality selection and EDR signal alignment are both critical for the performance, both with statistical significance. Conclusion. The sync-ensembled EDR provides robust respiratory information from electrocardiogram. Significance. Phase synchronization is not only theoretically rigorous but also practical to design a robust EDR.

Forced synchronization of self-excited chaotic thermoacoustic oscillations

We experimentally investigate the forced synchronization of a self-excited chaotic thermoacoustic oscillator with two natural frequencies, $f_1$ and $f_2$ . On increasing the forcing amplitude, $\epsilon _f$ , at a fixed forcing frequency, $f_f$ , we find two different types of synchronization: (i) $f_f/f_1 = 1:1$ or $2:1$ chaos-destroying synchronization (CDS), and (ii) phase synchronization of chaos (PSC). En route to $1:1$ CDS, the system transitions from an unforced chaotic state ( ${\rm {CH}}_{1,2}$ ) to a forced chaotic state ( ${\rm {CH}}_{1,2,f}$ ), then to a two-frequency quasiperiodic state where chaos is destroyed ( $\mathbb {T}^2_{2,f}$ ), and finally to a phase-locked period-1 state ( ${\rm {P1}}_f$ ). The route to $2:1$ CDS is similar, but the quasiperiodic state hosts a doubled torus $(2\mathbb {T}^2_{2,f})$ that transforms into a phase-locked period-2 orbit $({\rm {P2}}_f)$ when CDS occurs. En route to PSC, the system transitions to a forced chaotic state ( ${\rm {CH}}_{1,2,f}$ ) followed by a phase-locked chaotic state, where $f_1$ , $f_2$ and $f_f$ still coexist but their phase difference remains bounded. We find that the maximum reduction in thermoacoustic amplitude occurs near the onset of CDS, and that the critical $\epsilon _f$ required for the onset of CDS does not vary significantly with $f_f$ . We then use two unidirectionally coupled Anishchenko–Astakhov oscillators to phenomenologically model the experimental synchronization dynamics, including (i) the route to $1:1$ CDS, (ii) various phase dynamics, such as phase drifting, slipping and locking, and (iii) the thermoacoustic amplitude variations in the $f_f/f_1$ – $\epsilon _f$ plane. This study extends the applicability of open-loop control further to a chaotic thermoacoustic system, demonstrating (i) the feasibility of using an existing actuation strategy to weaken aperiodic thermoacoustic oscillations, and (ii) the possibility of developing new active suppression strategies based on both established and emerging methods of chaos control.

Contribution of positive affect in infant directed speech: what do amplitude modulations patterns suggest?

Speech perception relies heavily on cortical entrainment of amplitude modulations in speech, which occur at different rates. Following a study by Leong et al. (2017) showing slower modulations have higher power than faster modulations in infant directed speech (IDS), we hypothesized that positive emotions in IDS might drive this pattern. Using the same analyses (spectral amplitude modulation phase hierarchy method and phase synchronization index (PSI) (Leong and Goswami, 2015)), we compared the power of isolated modulation rates (synchronous with neural oscillations) and the synchrony between them in IDS and adult directed speech (ADS), using English stimuli from Many Babies Consortium (Frank et al., 2020). We repeated the same analyses comparing happy and neutral ADS using stimuli of four native English speakers (Pell et al., 2009). Our analysis did not uncover significant power differences between IDS and ADS. However, it revealed happy ADS has higher power at slower rates, with the reversed pattern for neutral ADS (p < 0.001). PSI was higher for two faster rates in neutral ADS (p < 0.0001), as reported by Leong et al. comparing IDS versus ADS. These findings reveal novel acoustic features of vocal emotions that might be important in attracting infant attention to IDS.

Distinct and common mechanisms of cross-model semantic conflict and response conflict in an auditory relevant task.

The mechanisms of semantic conflict and response conflict in the Stroop task have mainly been investigated in the visual modality. However, the understanding of these mechanisms in cross-modal modalities remains limited. In this electroencephalography (EEG) study, an audiovisual 2-1 mapping Stroop task was utilized to investigate whether distinct and/or common neural mechanisms underlie cross-modal semantic conflict and response conflict. The response time data showed significant effects on both cross-modal semantic and response conflicts. Interestingly, the magnitude of semantic conflict was found to be smaller in the fast response time bins than in the slow response time bins, whereas no such difference was observed for response conflict. The EEG data demonstrated that cross-modal semantic conflict specifically increased the N450 amplitude. However, cross-modal response conflict specifically enhanced theta band power and theta phase synchronization between the medial frontal cortex (MFC) and lateral prefrontal electrodes as well as between the MFC and motor electrodes. In addition, both cross-modal semantic conflict and response conflict led to a decrease in P3 amplitude. Taken together, these findings provide cross-modal evidence for domain-specific mechanism in conflict detection and suggest both domain-specific and domain-general mechanisms exist in conflict resolution.

Intermittent phase dynamics of non-autonomous oscillators through time-varying phase

Oscillatory dynamics pervades the universe, appearing in systems of all scales. Whilst autonomous oscillatory dynamics has been extensively studied and is well understood, the very important problem of non-autonomous oscillatory dynamics is less well understood. Here, we provide a framework for non-autonomous oscillatory dynamics, within which we can define intermittent phenomena such as intermittent phase synchronisation. Moreover, we demonstrate this framework with a coupled pair of non-autonomous phase oscillators as well as a higher-dimensional system comprising of two interacting phase-oscillator networks.

Unmanned Airborne Bistatic Interferometric Synthetic Aperture Radar Data Processing Method Using Bi-Directional Synchronization Chain Signals

The bistatic Interferometric Synthetic Aperture Radar (InSAR) system can overcome the physical limitations imposed by the baseline of monostatic dual-antenna InSAR. It provides greater flexibility and can enhance elevation measurement accuracy through a well-designed baseline configuration. Unmanned aerial vehicles (UAVs) equipped with bistatic InSAR, having relatively low cost and high flexibility, are useful for mapping and land resource exploration. However, due to challenges including spatiotemporal synchronization and motion errors, there are limited reports on UAV-borne bistatic InSAR. This paper proposes a comprehensive method for processing data from small UAV-borne bistatic InSAR by integrating two-way synchronization chain signals. The proposed method includes compensation for time and phase synchronization errors, trajectory refinement with synchronized chain and Position and Orientation System (POS) data, high-precision bistatic InSAR imaging, and interferometric processing. Height inversion results based on the proposed method are also provided, which demonstrate the effectiveness of the proposed method in improving the accuracy of interferometric measurement at calibration points from 0.66 m to 0.42 m.

Association of brain functional connectivity with neurodevelopmental outcomes in healthy full-term newborns

ObjectiveTo study the association between neurodevelopmental outcomes and functional brain connectivity (FBC) in healthy term infants. MethodsThis is a retrospective study of prospectively collected High-density electroencephalography (HD-EEG) from newborns within 72 hours from birth. Developmental assessments were performed at two years of age using the Bayley Scales of Infant Development-III (BSID-III) measuring cognitive, language, motor, and socio-emotional scores. The FBC was calculated using phase synchronization analysis of source signals in delta, theta, alpha, beta, and gamma frequency bands and its association with neurodevelopmental score was assessed with stepwise regression. Results47/163 had both HD-EEG and BSID-III scores. The FBC of frontal region was associated with cognitive score in the theta band (corrected p, regression coefficients range: p < 0.01, 1.66–1.735). Language scores were significantly associated with connectivity in all frequency bands, predominantly in the left hemisphere (p < 0.01, −2.74–2.40). The FBC of frontal and occipital brain regions of both hemispheres was related to motor score and socio-emotional development in theta, alpha, and gamma frequency bands (p < 0.01, −2.16–2.97). ConclusionsFunctional connectivity of higher-order processing is already present at term age. SignificanceThe FBC might be used to guide interventions for optimizing subsequent neurodevelopment even in low-risk newborns.

Simultaneous control of quantum phase synchronization and entanglement dynamics in a gain-loss optomechanical cavity system

Simultaneous control of quantum phase synchronization and entanglement dynamics in a gain-loss optomechanical cavity system

Deep learning approach for detection of unfavorable driving state based on multiple phase synchronization between multi-channel EEG signals

In recent years, electroencephalogram (EEG) signals have gained significant popularity in the detection and recognition of drivers' unfavorable driving states (UDS) and related aspects. However, the methods that rely on traditional EEG features and evaluate different electrodes or brain regions separately have somewhat limited the further development of recognition effectiveness. To address this, this study analyzes the phase relationships between electrodes in EEG signals to reveal the functional networks and connectivity patterns within the brain. Three phase synchronization (PS) methods, namely phase locking value (PLV), corrected imaginary phase locking value (CIPLV), and weighted phase lag index (WPLI), are used to construct connectivity matrices and networks in six classic sub-rhythmic bands. Additionally, a 2D convolutional neural network (CNN) with fewer learning parameters is designed to automatically learn high-level abstractions and the most discriminative features, thereby avoiding the laborious and subjective process of manual feature extraction. The proposed method has been compared with traditional classification algorithms using a leave-one-out cross-validation strategy. The comparative results indicate that our proposed approach, which combines WPLI phase synchronization in the gamma1 sub-rhythmic band with a pyramid-structured CNN model, achieves significantly higher accuracy in recognizing drivers' UDS than other conventional methods through a one-way analysis of variance (ANOVA) followed by post hoc multiple comparisons with Tukey analysis. Furthermore, our proposed 2D-CNN model contains fewer parameters, making it more competitive for further practical applications in real-world driving scenarios.

Math on cortex-enhanced delta phase synchrony in math experts during long and complex math demonstrations.

Neural oscillations are important for working memory and reasoning and they are modulated during cognitively challenging tasks, like mathematics. Previous work has examined local cortical synchrony on theta (4-8Hz) and alpha (8-13Hz) bands over frontal and parietal electrodes during short mathematical tasks when sitting. However, it is unknown whether processing of long and complex math stimuli evokes inter-regional functional connectivity. We recorded cortical activity with EEG while math experts and novices watched long (13-68seconds) and complex (bachelor-level) math demonstrations when sitting and standing. Fronto-parietal connectivity over the left hemisphere was stronger in math experts than novices reflected by enhanced delta (0.5-4Hz) phase synchrony in experts. Processing of complex math tasks when standing extended the difference to right hemisphere, suggesting that other cognitive processes, such as maintenance of body balance when standing, may interfere with novice's internal concentration required during complex math tasks more than in experts. There were no groups differences in phase synchrony over theta or alpha frequencies. These results suggest that low-frequency oscillations modulate inter-regional connectivity during long and complex mathematical cognition and demonstrate one way in which the brain functions of math experts differ from those of novices: through enhanced fronto-parietal functional connectivity.

Amygdala-hippocampus somatostatin interneuron beta-synchrony underlies a cross-species biomarker of emotional state

Emotional responses arise from limbic circuits including the hippocampus and amygdala. In the human brain, beta-frequency communication between these structures correlates with self-reported mood and anxiety. However, both the mechanism and significance of this biomarker as a readout vs. driver of emotional state remain unknown. Here, we show that beta-frequency communication between ventral hippocampus and basolateral amygdala also predicts anxiety-related behavior in mice, both on long timescales (∼30min) and immediately preceding behavioral choices. Genetically encoded voltage indicators reveal that this biomarker reflects synchronization between somatostatin interneurons across both structures. Indeed, synchrony between these neurons dynamically predicts approach-avoidance decisions, and optogenetically shifting the phase of synchronization by just 25ms is sufficient to bidirectionally modulate anxiety-related behaviors. Thus, back-translation establishes a human biomarker as a causal determinant (not just predictor) of emotional state, revealing a novel mechanism whereby interregional synchronization that is frequency, phase, and cell type specific controls emotional processing.

Widespread slow oscillations support interictal epileptiform discharge networks in focal epilepsy

Interictal epileptiform discharges (IEDs) often co-occur across spatially-separated cortical regions, forming IED networks. However, the factors prompting IED propagation remain unelucidated. We hypothesized that slow oscillations (SOs) might facilitate IED propagation. Here, the amplitude and phase synchronization of SOs preceding propagating and non-propagating IEDs were compared in 22 patients with focal epilepsy undergoing intracranial electroencephalography (EEG) evaluation. Intracranial channels were categorized into the irritative zone (IZ) and normal zone (NOZ) regarding the presence of IEDs. During wakefulness, we found that pre-IED SOs within the IZ exhibited higher amplitudes for propagating IEDs than non-propagating IEDs (delta band: p = 0.001, theta band: p < 0.001). This increase in SOs was also concurrently observed in the NOZ (delta band: p = 0.04). Similarly, the inter-channel phase synchronization of SOs prior to propagating IEDs was higher than those preceding non-propagating IEDs in the IZ (delta band: p = 0.04). Through sliding window analysis, we observed that SOs preceding propagating IEDs progressively increased in amplitude and phase synchronization, while those preceding non-propagating IEDs remained relatively stable. Significant differences in amplitude occurred approximately 1150 ms before IEDs. During non-rapid eye movement (NREM) sleep, SOs on scalp recordings also showed higher amplitudes before intracranial propagating IEDs than before non-propagating IEDs (delta band: p = 0.006). Furthermore, the analysis of IED density around sleep SOs revealed that only high-amplitude sleep SOs demonstrated correlation with IED propagation. Overall, our study highlights that transient but widely distributed SOs are associated with IED propagation as well as generation in focal epilepsy during sleep and wakefulness, providing new insight into the EEG substrate supporting IED networks.

Time-varying phase synchronization of resting-state functional magnetic resonance imaging reveals a shift toward self-referential processes during sustained pain.

Growing evidence has suggested that time-varying functional connectivity between different brain regions might underlie the dynamic experience of pain. This study used a novel, data-driven framework to characterize the dynamic interactions of large-scale brain networks during sustained pain by estimating recurrent patterns of phase-synchronization. Resting-state functional magnetic resonance imaging signals were collected from 50 healthy participants before (once) and after (twice) the onset of sustained pain that was induced by topical application of capsaicin cream. We first decoded the instantaneous phase of neural activity and then applied leading eigenvector dynamic analysis on the time-varying phase-synchronization. We identified 3 recurrent brain states that show distinctive phase-synchronization. The presence of state 1, characterized by phase-synchronization between the default mode network and auditory, visual, and sensorimotor networks, together with transitions towards this brain state, increased during sustained pain. These changes can account for the perceived pain intensity and reported unpleasantness induced by capsaicin application. In contrast, state 3, characterized by phase-synchronization between the cognitive control network and sensory networks, decreased after the onset of sustained pain. These results are indicative of a shift toward internally directed self-referential processes (state 1) and away from externally directed cognitive control processes (state 3) during sustained pain.

MEMS-based two-photon microscopy with Lissajous scanning and image reconstruction under a feed-forward control strategy.

Two-photon microscopy (TPM) based on two-dimensional micro-electro-mechanical (MEMS) system mirrors shows promising applications in biomedicine and the life sciences. To improve the imaging quality and real-time performance of TPM, this paper proposes Lissajous scanning control and image reconstruction under a feed-forward control strategy, a dual-parameter alternating drive control algorithm and segmented phase synchronization mechanism, and pipe-lined fusion-mean filtering and median filtering to suppress image noise. A 10 fps frame rate (512 × 512 pixels), a 140 µm × 140 µm field of view, and a 0.62 µm lateral resolution were achieved. The imaging capability of MEMS-based Lissajous scanning TPM was verified by ex vivo and in vivo biological tissue imaging.

OPM-MEG Measuring Phase Synchronization on Source Time Series: Application in Rhythmic Median Nerve Stimulation.

The magnetoencephalogram (MEG) based on array optically pumped magnetometers (OPMs) has the potential of replacing conventional cryogenic superconducting quantum interference device. Phase synchronization is a common method for measuring brain oscillations and functional connectivity. Verifying the feasibility and fidelity of OPM-MEG in measuring phase synchronization will help its widespread application in the study of aforementioned neural mechanisms. The analysis method on source-level time series can weaken the influence of instantaneous field spread effect. In this paper, the OPM-MEG was used for measuring the evoked responses of 20Hz rhythmic and arrhythmic median nerve stimulation, and the inter-trial phase synchronization (ITPS) and inter-reginal phase synchronization (IRPS) of primary somatosensory cortex (SI) and secondary somatosensory cortex (SII) were analysed. The results find that under rhythmic condition, the evoked responses of SI and SII show continuous oscillations and the effect of resetting phase. The values of ITPS and IRPS significantly increase at the stimulation frequency of 20Hz and its harmonic of 40Hz, whereas the arrhythmic stimulation does not exhibit this phenomenon. Moreover, in the initial stage of stimulation, the ITPS and IRPS values are significantly higher at Mu rhythm in the rhythmic condition compared to arrhythmic. In conclusion, the results demonstrate the ability of OPM-MEG in measuring phase pattern and functional connectivity on source-level, and may also prove beneficial for the study on the mechanism of rhythmic stimulation therapy for rehabilitation.