Pairwise Synchronization Research Articles

Pairwise synchronization of second-order matrix-weighted networks

Abstract This paper deals with the pairwise synchronization of second-order linear time invariant (LTI) systems with incommensurable outputs through a matrix-weighted graph. The pairwise synchronization here means that the relative outputs have pairwise synchronized solutions for the identical LTI systems. For the matrix-weighted network, some necessary and sufficient conditions on the pairwise synchronization are given by means of the Jordan form, matrix decomposition and effective conductance. Moreover, the relationship between the global synchronization and the connectivity of its interconnection graph is also discussed. Examples and simulations are shown to verify the theoretical results.

Low-order modeling of collective dynamics of four ring-coupled turbulent thermoacoustic oscillators

We investigate the low-order modeling of collective dynamics in a can-annular combustor consisting of four ring-coupled turbulent lean-premixed combustors. Each combustor is treated as an individual thermoacoustic oscillator, and the entire combustion system is modeled using four Van der Pol oscillators ring-coupled with dissipative, time-delay, and reactive coupling terms. We show that this model, despite its simplicity, can reproduce many collective dynamics observed in experiments under various combinations of equivalence ratios and combustor lengths, such as 2-can anti-phase synchronization, alternating anti-phase synchronization, pairwise anti-phase synchronization, spinning azimuthal mode, and 4 steady thermoacoustic oscillators. The phase relationship in the majority of cases can be quantitatively modeled. Moreover, by incorporating a reactive coupling term, the model is able to reproduce the frequency shift observed experimentally. This study demonstrates the feasibility of using a simple low-order model to reproduce collective dynamics in complex turbulent combustion systems. This suggests that this model could be used (i) to facilitate the interpretation of experimental data within the synchronization framework, (ii) to identify potential parameter regimes leading to amplitude death, and (iii) to serve as a basis for modeling the collective dynamics observed in more complicated multi-combustors.

Stationarity and cycles in the energy consumption in the United States

The purpose of this paper is twofold: analyzing stationarity of energy consumption by source in the United States and studying their cycles and pairwise synchronization. We study a panel of nine time series of monthly energy consumption for the period 1973–2022. Four of the series (namely coal, natural gas, petroleum, and nuclear electric power consumption) are non-renewables, whereas the remaining ones (hydroelectric power, geothermal, biomass, solar, and wind energy consumption) are renewable energy sources. We employ a nonparametric, panel stationarity testing approach. The results indicate that most of the series may be trend-stationarity, with nuclear and geothermal energy consumption being the only exceptions. Additionally, a study on potential cycles in the series of energy consumption by source is carried out, and subsequently we analyze pairwise concordance between states of different energy sources and between states of energy sources and the business cycle. Significant correlations are detected in the latter analysis, which are positive in the case of fossil fuel sources and negative for two renewable sources, namely geothermal and biomass energy consumption.

Inferring connectivity of an oscillatory network via the phase dynamics reconstruction

We review an approach for reconstructing oscillatory networks’ undirected and directed connectivity from data. The technique relies on inferring the phase dynamics model. The central assumption is that we observe the outputs of all network nodes. We distinguish between two cases. In the first one, the observed signals represent smooth oscillations, while in the second one, the data are pulse-like and can be viewed as point processes. For the first case, we discuss estimating the true phase from a scalar signal, exploiting the protophase-to-phase transformation. With the phases at hand, pairwise and triplet synchronization indices can characterize the undirected connectivity. Next, we demonstrate how to infer the general form of the coupling functions for two or three oscillators and how to use these functions to quantify the directional links. We proceed with a different treatment of networks with more than three nodes. We discuss the difference between the structural and effective phase connectivity that emerges due to high-order terms in the coupling functions. For the second case of point-process data, we use the instants of spikes to infer the phase dynamics model in the Winfree form directly. This way, we obtain the network’s coupling matrix in the first approximation in the coupling strength.

New timestamp mark–based energy efficient time synchronization method for wireless sensor networks

Aimed at the demands of wireless sensor networks for high energy-efficient time synchronization, the reduction of synchronization energy consumption is studied from the aspects of both accurate timestamps marking and synchronous information transmission mechanism. First, the network is divided into several parent–child groups periodically. The group-wise pair selection algorithm is used to select the network’s pairwise synchronization nodes, and chain-type network topology is thus generated. Second, the sequential multi-hop synchronization algorithm is introduced to realize the synchronization information exchange among pairwise synchronization nodes. The overhearing synchronization (OS) nodes obtain the synchronization information packet based on a one-way overhearing mechanism. Moreover, the accurate acquisition of the synchronization ack packet’s timestamp is carried out through the use of receiving-time-plus-fixed-delay mode. Third, the joint maximum likelihood method and the minimum variance unbiased estimation method are used to estimate the clock offsets of pairwise synchronization nodes and overhearing nodes to the parent nodes, respectively, based on which the child nodes adjust their local virtual clocks. Periodically, the pairwise synchronization nodes initiate the network’s time synchronization, estimate, and broadcast the relative offset to the gateway node, assisting the upper layer child nodes in synchronizing to the gateway node. Simulation results show that the proposed method not only achieves the millisecond level synchronization accuracy but also reduces the synchronization energy consumption and thus improves the network lifetime.

Ordinal synchronization and typical states in high-frequency digital markets

In this paper we study Algorithmic High-Frequency Financial Markets as dynamical networks. After an individual analysis of 24 stocks of the US market during a trading year of fully automated transactions by means of ordinal pattern series, we define an information-theoretic measure of pairwise synchronization for time series which allows us to study this subset of the US market as a dynamical network. We apply to the resulting network a couple of clustering algorithms in order to detect collective market states, characterized by their degree of centralized or decentralized synchronicity. This collective analysis has shown to reproduce, classify and explain the anomalous behavior previously observed at the individual level. We also find two whole coherent seasons of highly centralized and decentralized synchronicity, respectively. Finally, we model these states dynamics through a simple Markov model.

Change in brain electrical activity connectivity in migraine patients without aura

Objective: In this study, we consider how the structure of the brain EEG activity changes in patients with migraine, compared with virtually healthy volunteers without complaints of acute or chronic headache. Materials and Methods. The study of the connectivity of EEG activity was carried out on the basis of an objective assessment of pairwise synchronization between different recording channels, for which we used a method based on wavelet bicoherence. Results. Within the framework of the performed experimental study, we demonstrated an increased reactivity in the structure of connections in brain electrical activity of the patients experiencing a weak visual impact. Conclusion. A prospective study could determine the value of the described diagnostic procedure in support of the clinical decision on appropriate pharmacological and non-pharmacological prophylactic measures.

State-Dependent Synchrony and Functional Connectivity in the Primary and Secondary Whisker Somatosensory Cortices.

Synchronized activity plays an important role in sensory coding and memory and is a hallmark of functional network connectivity. However, the effect of sensory activation on synchronization and cortical functional connectivity is largely unknown. In this study, we investigated the effect of whisker activation on synchronization and functional connectivity of the primary (wS1) and secondary (wS2) whisker somatosensory cortices at the single-cell level. The results showed that during the spontaneous pre-stimulus state, neurons tended to be functionally connected with nearby neurons which shared similar tuning characteristics. Whisker activation using either ramp-and-hold stimulation or artificial whisking against sandpaper has significantly reduced the average overall pairwise synchronization and functional connectivity within the wS1 barrel and wS2 cortices. Whisker stimulation disconnected approximately a third of neuronal pairs that were functionally connected during the unstimulated state. Nearby neurons with congruent tuning properties were more likely to remain functionally connected during whisker activation. The findings of this study indicated that cortical somatosensory networks are organized in non-random small world networks composed of neurons sharing relatively similar tuning properties. Sensory whisker activation intensifies these properties and further subdivides the cortical network into smaller more functionally uniform subnetworks, which possibly serve to increase the computational capacity of the network.

Relativistic Modelling for Accurate Time Transfer via Optical Inter-Satellite Links

The DLR Institute for Communication and Navigation is currently working on a new GNSS architecture that enables accurate autonomous inter-satellite synchronization at picosecond-level. Synchronization is achieved via time transfer techniques enabled by optical inter-satellite links (OISLs), paving the way for a system in which space (orbits) and time (synchronization) can be effectively separated, leading to a high level of synchronization throughout the constellation, which in turn greatly improves accurate orbit determination. This is possible provided that relativistic effects are adequately taken into account. This work focuses on a two-way time transfer scheme based on the exchange of time stamps via optical signals, which allows the synchronization of a GNSS satellite system with respect to a defined coordinate time with picosecond-level accuracy. We analyse the impact of relativistic effects in clock offset estimation between optically linked clocks: results show that to achieve synchronization at this level of accuracy it is necessary to account for terrestrial geopotential harmonics up to the third order while the gravitational influence of additional celestial bodies can be neglected. Relativistic delays in the propagation of electromagnetic waves through spacetime are also evaluated. It is shown that for a two-way synchronization method, the Euclidean expression for the propagation of light is sufficient to achieve picosecond synchronization, provided m-level orbit determination of both satellites is available, and the hardware delays are well calibrated to the targeted accuracy. Also, we show how to practically achieve autonomous synchronization via a sequence of pair-wise synchronizations across all satellites of the constellation.

On the characterization of cognitive tasks using activity-specific short-lived synchronization between electroencephalography channels

Accurate characterization of brain activity during a cognitive task is challenging due to the dynamically changing and the complex nature of the brain. The majority of the proposed approaches assume stationarity in brain activity and disregard the systematic timing organization among brain regions during cognitive tasks. In this study, we propose a novel cognitive activity recognition method that captures the activity-specific timing parameters from training data that elicits maximal average short-lived pairwise synchronization between electroencephalography signals. We evaluated the characterization power of the activity-specific timing parameter triplets in a motor imagery activity recognition framework. The activity-specific timing parameter triplets consist of latency of the maximally synchronized signal segments from activity onset Δt, the time lag between maximally synchronized signal segments τ, and the duration of the maximally synchronized signal segments w. We used cosine-based similarity, wavelet bi-coherence, phase-locking value, phase coherence value, linearized mutual information, and cross-correntropy to calculate the channel synchronizations at the specific timing parameters. Recognition performances as well as statistical analyses on both BCI Competition-III dataset IVa and PhysioNet Motor Movement/Imagery dataset, indicate that the inter-channel short-lived synchronization calculated using activity-specific timing parameter triplets elicit significantly distinct synchronization profiles for different motor imagery tasks and can thus reliably be used for cognitive task recognition purposes.

Pair Nodes Clock Synchronization Algorithm Based on Kalman Filter for Underwater Wireless Sensor Networks.

Time synchronization is the basis of many applications. Aiming at the limitations of the existing clock synchronization algorithms in underwater wireless sensor networks, we propose a pairwise synchronization algorithm called K-Sync, which is based on the Kalman filter. The algorithm does not need the assistance of the position sensor or the speed sensor, and the high time synchronization accuracy can be realized only by utilizing the time-stamps information in the process of message exchange. The K-Sync uses the general constraints of the motion characteristics of the sensor nodes to establish the recursive equations of the clock skew, clock offset, relative mobility velocity, and relative distance. At the same time, the time-stamps are viewed as the observation variables and the system observation equation is obtained. The K-Sync estimates the normalized clock skew and offset of the node via the Kalman filter to achieve high-precision clock synchronization between the two nodes. The simulation shows that the K-Sync has obvious advantages in the key indicators such as the estimated accuracy of clock skew and clock offset, convergence speed, etc. In addition, the K-Sync is more robust to a variety of underwater motion scenes.

Synchronization in 5G networks: a hybrid Bayesian approach toward clock offset/skew estimation and its impact on localization

Clock synchronization has always been a major challenge when designing wireless networks. This work focuses on tackling the time synchronization problem in 5G networks by adopting a hybrid Bayesian approach for clock offset and skew estimation. Furthermore, we provide an in-depth analysis of the impact of the proposed approach on a synchronization-sensitive service, i.e., localization. Specifically, we expose the substantial benefit of belief propagation (BP) running on factor graphs (FGs) in achieving precise network-wide synchronization. Moreover, we take advantage of Bayesian recursive filtering (BRF) to mitigate the time-stamping error in pairwise synchronization. Finally, we reveal the merit of hybrid synchronization by dividing a large-scale network into local synchronization domains and applying the most suitable synchronization algorithm (BP- or BRF-based) on each domain. The performance of the hybrid approach is then evaluated in terms of the root mean square errors (RMSEs) of the clock offset, clock skew, and the position estimation. According to the simulations, in spite of the simplifications in the hybrid approach, RMSEs of clock offset, clock skew, and position estimation remain below 10 ns, 1 ppm, and 1.5 m, respectively.

Global Study of Human Heart Rhythm Synchronization with the Earth’s Time Varying Magnetic Field

Changes in geomagnetic conditions have been shown to affect the rhythms produced by the brain and heart and that human autonomic nervous system activity reflected in heart rate variability (HRV) over longer time periods can synchronize to changes in the amplitude of resonant frequencies produced by geomagnetic field-line and Schumann resonances. During a 15-day period, 104 participants located in California, Lithuania, Saudi Arabia, New Zealand, and England underwent continuous ambulatory HRV monitoring. The local time varying magnetic field (LMF) intensity was obtained using a time synchronized and calibrated network of magnetometers located at five monitoring sites in the same geographical locations as the participant groups. This paper focuses on the results of an experiment conducted within the larger study where all of the participants simultaneously did a heart-focused meditation called a Heart Lock-In (HLI) for a 15-min period. The participant’s level of HRV coherence and HRV synchronization to each other before, during and after the HLI and the synchronization between participants’ HRV and local time varying magnetic field power during each 24-h period were computed for each participant and group with near-optimal chaotic attractor embedding techniques. In analysis of the participants HRV coherence before, during and after the HLI, most of the groups showed significantly increased coherence during the HLI period. The pairwise heart rhythm synchronization between participants’ in each group was assessed by determining the Euclidean distance of the optimal time lag vectors of each participant to all other participants in their group. The group member’s heart rhythms were significantly more synchronized with each other during the HLI period in all the groups. The participants’ daily LMF-HRV-synchronization was calculated for each day over an 11-day period, which provided a 5-day period before, the day of and 5-days after the HLI day. The only day where all the groups HRV was positively correlated with the LMF was on the day of the HLI and the synchronization between the HRV and LMF for all the groups was significantly higher than most of the other days.

Business cycle synchronization among the US states: spatial effects and regional determinants

ABSTRACT This paper investigates the extent and determinants of business cycle synchronization among the US states during the period 2002–11. Phase synchronization is not measured based on one national reference series, but rather is assessed using pairwise synchronization indicators computed over the business cycles of all US state pairs. The analysis is based on a natural and intuitive measure of synchronization: the fraction of observations when the cyclical phase is the same for both states in each state pair. Synchronization indicators have a spatially correlated structure. The economic determinants of synchronization are studied using spatial econometric models. Business cycles are more synchronized between those states characterized by strong commercial links and a similar structure in terms of industrialization, labour market characteristics and openness.

A Novel Reliable Adaptive Beacon Time Synchronization Algorithm for Large-Scale Vehicular Ad Hoc Networks

The time synchronization in vehicular ad hoc networks (VANETs) has gained significant attention in recent times. In this paper, we focus on the time synchronization in large-scale VANETs and propose an adaptive beacon time synchronization (ABTS) algorithm to enhance timing message synchronization. ABTS algorithm selects the best time synchronization pairs to decrease the number of timing messages transmitted. To guarantee the reliability of synchronization, the clock offset of the connected vehicles periodically readjust to provide a better degree of synchronization accuracy with minimum energy consumption. Based on two-way timing message synchronization, we derive maximum likelihood (ML) estimation and its equivalent Cramer-Rao lower bound (CRLB) for clock offset design in the generalized sender-to-receiver system by assuming a Gaussian noise model. We propose node pair selection algorithms to improve pairwise beacon message timing synchronization. The simulation results validate that our proposed ABTS algorithm performs better than other protocols in terms of synchronization accuracy, the rate of convergence and energy efficiency.

Fiscal policy, government size and EMU business cycle synchronization

AbstractWe provide new evidence on the effects of fiscal policy and government size on pairwise business cycle synchronization in EMU. A novel time‐varying framework is employed to estimate business cycle synchronization and subsequently a panel approach is used to establish the role of fiscal variables in determining the pairwise synchronization observations across time. The findings suggest similarities in the size of the public sector, yet divergence in fiscal policy stance, matter for the determination of business cycle synchronization. Hence, increased fiscal federalism in EMU will contribute to increased business cycle synchronization. Our results remain robust to different specifications and sub‐periods.

Evaluation of synchronization measures for capturing the lagged synchronization between EEG channels: A cognitive task recognition approach

During cognitive, perceptual and sensory tasks, connectivity profile changes across different regions of the brain. Variations of such connectivity patterns between different cognitive tasks can be evaluated using pairwise synchronization measures applied to electrophysiological signals, such as electroencephalography (EEG). However, connectivity-based task recognition approaches achieving viable recognition performance have been lacking from the literature. By using several synchronization measures, we identify time lags between channel pairs during different cognitive tasks.We employed mutual information, cross correntropy, cross correlation, phase locking value, cosine similarity and nonlinear interdependence measures. In the training phase, for each type of cognitive task, we identify the time lags that maximize the average synchronization between channel pairs. These lags are used to calculate pairwise synchronization values with which we construct the train and test feature vectors for recognition of the cognitive task carried out using Fisher's linear discriminant (FLD) analysis.We tested our framework in a motor imagery activity recognition scenario on PhysioNet Motor Movement/Imagery and BCI Competition-III Ⅳa datasets. For PhysioNet dataset, average performance results ranging between % 51 and % 61 across 20 subjects. For BCI Competition-Ⅲ dataset, we achieve an average recognition performance of % 76 which is above the minimum reliable communication rate (% 70).We achieved an average accuracy over the minimum reliable communication rate on the BCI Competition-Ⅲ dataset. Performance levels were lower on the PhysioNet dataset. These results indicate that a viable task recognition system is achievable using pairwise synchronization measures evaluated at the proper task specific lags.

CRONOS

Data synchronization is crucial in ubiquitous computing systems, where heterogeneous sensor devices, modalities, and different communication capabilities and protocols are the norm. A common notion of time among devices is required to make sense of their sensing data. Traditional synchronization methods rely on wireless communication between devices to synchronize, potentially incurring computational and power costs. Furthermore, they are unsuitable for synchronizing data streams that have already been collected. We present CRONOS: a post-hoc, data-driven framework for sensor data synchronization for wearable and Internet-of-Things devices that takes advantage of independent, omni-present motion events in the data streams of two or more sensors. Experimental results on pairwise and multi-sensor synchronization show a drift improvement as high as 98% and a mean absolute synchronization error of approximately 6ms for multi-sensor synchronization with sensors sampling at 100Hz.

Multifractal Dynamic Functional Connectivity in the Resting-State Brain.

Assessing the functional connectivity (FC) of the brain has proven valuable in enhancing our understanding of brain function. Recent developments in the field demonstrated that FC fluctuates even in the resting state, which has not been taken into account by the widely applied static approaches introduced earlier. In a recent study using functional near-infrared spectroscopy (fNIRS) global dynamic functional connectivity (DFC) has also been found to fluctuate according to scale-free i.e., fractal dynamics evidencing the true multifractal (MF) nature of DFC in the human prefrontal cortex. Expanding on these findings, we performed electroencephalography (EEG) measurements in 14 regions over the whole cortex of 24 healthy, young adult subjects in eyes open (EO) and eyes closed (EC) states. We applied dynamic graph theoretical analysis to capture DFC by computing the pairwise time-dependent synchronization between brain regions and subsequently calculating the following dynamic graph topological measures: Density, Clustering Coefficient, and Efficiency. We characterized the dynamic nature of these global network metrics as well as local individual connections in the networks using focus-based multifractal time series analysis in all traditional EEG frequency bands. Global network topological measures were found fluctuating–albeit at different extent–according to true multifractal nature in all frequency bands. Moreover, the monofractal Hurst exponent was found higher during EC than EO in the alpha and beta bands. Individual connections showed a characteristic topology in their fractal properties, with higher autocorrelation owing to short-distance connections–especially those in the frontal and pre-frontal cortex–while long-distance connections linking the occipital to the frontal and pre-frontal areas expressed lower values. The same topology was found with connection-wise multifractality in all but delta band connections, where the very opposite pattern appeared. This resulted in a positive correlation between global autocorrelation and connection-wise multifractality in the higher frequency bands, while a strong anticorrelation in the delta band. The proposed analytical tools allow for capturing the fine details of functional connectivity dynamics that are evidently present in DFC, with the presented results implying that multifractality is indeed an inherent property of both global and local DFC.

Chaos versus noise as drivers of multistability in neural networks.

The multistable behavior of neural networks is actively being studied as a landmark of ongoing cerebral activity, reported in both functional Magnetic Resonance Imaging (fMRI) and electro- or magnetoencephalography recordings. This consists of a continuous jumping between different partially synchronized states in the absence of external stimuli. It is thought to be an important mechanism for dealing with sensory novelty and to allow for efficient coding of information in an ever-changing surrounding environment. Many advances have been made to understand how network topology, connection delays, and noise can contribute to building this dynamic. Little or no attention, however, has been paid to the difference between local chaotic and stochastic influences on the switching between different network states. Using a conductance-based neural model that can have chaotic dynamics, we showed that a network can show multistable dynamics in a certain range of global connectivity strength and under deterministic conditions. In the present work, we characterize the multistable dynamics when the networks are, in addition to chaotic, subject to ion channel stochasticity in the form of multiplicative (channel) or additive (current) noise. We calculate the Functional Connectivity Dynamics matrix by comparing the Functional Connectivity (FC) matrices that describe the pair-wise phase synchronization in a moving window fashion and performing clustering of FCs. Moderate noise can enhance the multistable behavior that is evoked by chaos, resulting in more heterogeneous synchronization patterns, while more intense noise abolishes multistability. In networks composed of nonchaotic nodes, some noise can induce multistability in an otherwise synchronized, nonchaotic network. Finally, we found the same results regardless of the multiplicative or additive nature of noise.