Amplitude Synchronization Research Articles

Fractional-Order Tabu Learning Neuron Models and Their Dynamics

In this paper, by replacing the exponential memory kernel function of a tabu learning single-neuron model with the power-law memory kernel function, a novel Caputo’s fractional-order tabu learning single-neuron model and a network of two interacting fractional-order tabu learning neurons are constructed firstly. Different from the integer-order tabu learning model, the order of the fractional-order derivative is used to measure the neuron’s memory decay rate and then the stabilities of the models are evaluated by the eigenvalues of the Jacobian matrix at the equilibrium point of the fractional-order models. By choosing the memory decay rate (or the order of the fractional-order derivative) as the bifurcation parameter, it is proved that Hopf bifurcation occurs in the fractional-order tabu learning single-neuron model where the value of bifurcation point in the fractional-order model is smaller than the integer-order model’s. By numerical simulations, it is shown that the fractional-order network with a lower memory decay rate is capable of producing tangent bifurcation as the learning rate increases from 0 to 0.4. When the learning rate is fixed and the memory decay increases, the fractional-order network enters into frequency synchronization firstly and then enters into amplitude synchronization. During the synchronization process, the oscillation frequency of the fractional-order tabu learning two-neuron network increases with an increase in the memory decay rate. This implies that the higher the memory decay rate of neurons, the higher the learning frequency will be.

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.

Synchronization measurement based on Poincaré’s sphere

Synchronization is an important phenomenon occurring in many complex systems, such as neural networks, power grids, or social networks. Various methods have been proposed to measure synchronization, each with its advantages and limitations. In this work, we introduce the Poincaré sphere as a generalized measure of synchronization, which provides a useful tool to visualize the similarities between oscillations. We propose the notion of “total synchronization,” which considers amplitude, frequency, and phase synchronization, all of which can be measured and visualized simultaneously on the Poincaré sphere. We show that visualizing oscillatory trajectories on the Poincaré sphere has advantages over the more typical two-dimensional representation, particularly in cases where a projection onto a two-dimensional space cannot capture the similarities between different oscillations. Furthermore, we apply this new synchronization measurement to linear and nonlinear oscillators and provide two concrete examples of its application in visualizing phase jitter in noisy oscillations and quantizing solutions of oscillator-based Ising machines. Our work demonstrates the usefulness of the Poincaré sphere as a generalized measure of synchronization and provides a new perspective on studying synchronization in complex systems.

ID: 208214 Comparison of Amplitude and Phase Synchronization in Detecting Functional Connectivity Alterations in Mesial Temporal Sclerosis

Temporal lobe epilepsy (TLE) is the most common form of refractory focal epilepsy1,2. Mesial temporal sclerosis (MTS) is a subtype of TLE and can cause severe complications3. Resting-state fMRI (rsfMRI) has been used to detect alterations in functional connectivity (FC) in patients with MTS4–6. Amplitude synchronization (AS) via seed-to-voxel analysis is a method used to detect FC from rsfMRI7,8. Phase synchronization (PS) is a technique used primarily with EEG to detect FC but has not been widely used in rsfMRI analysis9,10. In this study, we aimed to compare phase and amplitude synchronization in detecting temporal lobe FC alterations in MTS patients.

Resting-State fMRI Can Detect Alterations in Seizure Onset and Spread Regions in Patients with Non-Lesional Epilepsy: A Pilot Study.

Epilepsy is defined as non-lesional (NLE) when a lesion cannot be localized via standard neuroimaging. NLE is known to have a poor response to surgery. Stereotactic electroencephalography (sEEG) can detect functional connectivity (FC) between zones of seizure onset (OZ) and early (ESZ) and late (LSZ) spread. We examined whether resting-state fMRI (rsfMRI) can detect FC alterations in NLE to see whether noninvasive imaging techniques can localize areas of seizure propagation to potentially target for intervention. This is a retrospective study of 8 patients with refractory NLE who underwent sEEG electrode implantation and 10 controls. The OZ, ESZ, and LSZ were identified by generating regions around sEEG contacts that recorded seizure activity. Amplitude synchronization analysis was used to detect the correlation of the OZ to the ESZ. This was also done using the OZ and ESZ of each NLE patient for each control. Patients with NLE were compared to controls individually using Wilcoxon tests and as a group using Mann-Whitney tests. Amplitude of low-frequency fluctuations (ALFF), fractional ALFF (fALFF), regional homogeneity (ReHo), degree of centrality (DoC), and voxel-mirrored homotopic connectivity (VMHC) were calculated as the difference between NLE and controls and compared between the OZ and ESZ and to zero. A general linear model was used with age as a covariate with Bonferroni correction for multiple comparisons. Five out of 8 patients with NLE showed decreased correlations from the OZ to the ESZ. Group analysis showed patients with NLE had lower connectivity with the ESZ. Patients with NLE showed higher fALFF and ReHo in the OZ but not the ESZ, and higher DoC in the OZ and ESZ. Our results indicate that patients with NLE show high levels of activity but dysfunctional connections in seizure-related areas. rsfMRI analysis showed decreased connectivity directly between seizure-related areas, while FC metric analysis revealed increases in local and global connectivity in seizure-related areas. FC analysis of rsfMRI can detect functional disruption that may expose the pathophysiology underlying NLE.

Chimera states in multiplex networks: Chameleon-like across-layer synchronization.

Different across-layer synchronization types of chimera states in multilayer networks have been discovered recently. We investigate possible relations between them, for example, if the onset of some synchronization type implies the onset of some other type. For this purpose, we use a two-layer network with multiplex inter-layer coupling. Each layer consists of a ring of non-locally coupled phase oscillators. While oscillators in each layer are identical, the layers are made non-identical by introducing mismatches in the oscillators' mean frequencies and phase lag parameters of the intra-layer coupling. We use different metrics to quantify the degree of various across-layer synchronization types. These include phase-locking between individual interacting oscillators, amplitude and phase synchronization between the order parameters of each layer, generalized synchronization between the driver and response layer, and the alignment of the incoherent oscillator groups' position on the two rings. For positive phase lag parameter mismatches, we get a cascaded onset of synchronization upon a gradual increase of the inter-layer coupling strength. For example, the two order parameters show phase synchronization before any of the interacting oscillator pairs does. For negative mismatches, most synchronization types have their onset in a narrow range of the coupling strength. Weaker couplings can destabilize chimera states in the response layer toward an almost fully coherent or fully incoherent motion. Finally, in the absence of a phase lag mismatch, sufficient coupling turns the response dynamics into a replica of the driver dynamics with the phases of all oscillators shifted by a constant lag.

Improvements in classification of left and right foot motor intention using modulated steady-state somatosensory evoked potential induced by electrical stimulation and motor imagery.

In recent years, motor imagery-based brain-computer interface (MI-BCI) has been applied to motor rehabilitation in patients with motor dysfunction. However, traditional MI-BCI is rarely used for foot motor intention recognition because the motor cortex regions of both feet are anatomically close to each other, and traditional event-related desynchronization (ERD) patterns for MI-BCI have insufficient spatial discrimination. This study introduced steady-state somatosensory evoked potentials (SSSEPs) by synchronous bilateral feet electrical stimulation at different frequencies, which were used as carrier signals modulated by unilateral foot motor intention. Fifteen subjects participated in MI and MI-SSSEP tasks. A Riemannian geometry classifier with a task-related component analysis (TRCA) spatial filter was proposed to demodulate the variation in SSSEP features and discriminate the left and right foot motor intentions. The feature outcomes indicated that the amplitude and phase synchronization of the SSSEPs could be well modulated by unilateral foot MI tasks under the MI-SSSEP paradigm. The classification results revealed that the modulated SSSEP features played an important role in the recognition of left-right foot discrimination. Moreover, the proposed TRCA-based method outperformed the other three methods and improved the foot average classification accuracy to 81.07±13.29%, with the highest accuracy attained at 97.00%. Compared with the traditional MI paradigm, the foot motor intention recognition accuracy of the MI-SSSEP paradigm was significantly improved, from nearly 60% to more than 80%. This work provides a practical method for left-right foot motor intention recognition and expands the application of MI-BCI in the field of lower-extremity motor function rehabilitation.

Amplitude synchronization of spontaneous activity of medial and lateral temporal gyri reveals altered thalamic connectivity in patients with temporal lobe epilepsy

In this study, we examined whether amplitude synchronization of medial (MTL) and lateral (LTL) temporal lobes can detect unique alterations in patients with MTL epilepsy (mTLE) with mesial temporal sclerosis (MTS). This was a retrospective study of preoperative resting-state fMRI (rsfMRI) data from 31 patients with mTLE with MTS (age 23–69) and 16 controls (age 21–35). fMRI data were preprocessed based on a multistep preprocessing pipeline and registered to a standard space. Using each subject’s T1-weighted scan, the MTL and LTL were automatically segmented, manually revised and then fit to a standard space using a symmetric normalization registration algorithm. Dual regression analysis was applied on preprocessed rsfMRI data to detect amplitude synchronization of medial and lateral temporal segments with the rest of the brain. We calculated the overlapped volume ratio of synchronized voxels within specific target regions including the thalamus (total and bilateral). A general linear model was used with Bonferroni correction for covariates of epilepsy duration and age of patient at scan to statistically compare synchronization in patients with mTLE with MTS and controls, as well as with respect to whether patients remained seizure-free (SF) or not (NSF) after receiving epilepsy surgery. We found increased ipsilateral positive connectivity between the LTLs and the thalamus and contralateral negative connectivity between the MTLs and the thalamus in patients with mTLE with MTS compared to controls. We also found increased asymmetry of functional connectivity between temporal lobe subregions and the thalamus in patients with mTLE with MTS, with increased positive connectivity between the LTL and the lesional-side thalamus as well as increased negative connectivity between the MTL and the nonlesional-side thalamus. This asymmetry was also seen in NSF patients but was not seen in SF patients and controls. Amplitude synchronization was an effective method to detect functional connectivity alterations in patients with mTLE with MTS. Patients with mTLE with MTS overall showed increased temporal-thalamic connectivity. There was increased functional involvement of the thalamus in MTS, underscoring its role in seizure spread. Increased functional thalamic asymmetry patterns in NSF patients may have a potential role in prognosticating patient response to surgery. Elucidating regions with altered functional connectivity to temporal regions can improve understanding of the involvement of different regions in the disease to potentially target for intervention or use for prognosis for surgery. Future studies are needed to examine the effectiveness of using patient-specific abnormalities in patterns to predict surgical outcome.

Network synchronization deficits caused by dementia and Alzheimer's disease serve as topographical biomarkers: a pilot study.

Mild cognitive impairment (MCI) is known as an early stage of cognitive decline. Amnestic MCI (aMCI) is considered as the preliminary stage of dementia which may progress to Alzheimer’s disease (AD). While some aMCI patients may stay in this condition for years, others might develop dementia associated with AD. Early detection of MCI allows for potential treatments to prevent or decelerate the process of developing dementia. Standard methods of diagnosing MCI and AD employ structural (imaging), behavioral (cognitive tests), and genetic or molecular (blood or CSF tests) techniques. Our study proposes network-level neural synchronization parameters as topographical markers for diagnosing aMCI and AD. We conducted a pilot study based on EEG data recorded during an olfactory task from a group of elderly participants consisting of healthy individuals and patients of aMCI and AD to assess the value of different indicators of network-level phase and amplitude synchronization in differentiating the three groups. Significant differences were observed in the percent phase locking value, theta-gamma phase-amplitude coupling, and amplitude coherence between the groups, and classifiers were developed to differentiate the three groups based on these parameters. The observed differences in these indicators of network-level functionality of the brain can help explain the underlying processes involved in aMCI and AD.

Variable Data Rate Architectures in Optical LEO Direct-to-Earth Links: Design Aspects and System Analysis

In the frame of ongoing efforts between space agencies to define an on-off-keying-based optical low-Earth-orbit (LEO) direct-to-Earth (DTE) waveform, this paper offers an in-depth analysis of the Variable Data Rate (VDR) technique. VDR, in contrast to the currently adopted Constant Data Rate (CDR) approach, enables the optimization of the average throughput during a LEO pass over the optical ground station (OGS). The analysis addresses both critical link level aspects, such as receiver (time, frame, and amplitude) synchronization, as well as demonstrates the benefits stemming from employing VDR at system level.

Localization and diagnosis of abnormal channels in children with ASD based on WMSSE and ASI

BackgroundThe purpose of this study is to explore the differences of resting EEG in children with autism spectrum disorders and then analyze the sensitive channels with significant differences, to provide support for the accurate differential diagnosis of autism spectrum disorder (ASD). New methodBased on the weighted multi-scale sample entropy (WMSSE) algorithm and amplitude synchronization index (ASI) algorithm of EEG, this paper comprehensively evaluates the brain state of ASD children from the two aspects of brain function complexity and brain function synchronization connectivity. Further, by combining the support vector machine (SVM) classification model to explore the location of abnormal channels of ASD children and realize the diagnosis of ASD children. ResultsThe WMSSE of the ASD group was lower than that of the healthy group. Furthermore, there was a significant difference in the F3/F4 channels and F7/F8 channels (P < 0.05), and the synchronization of the brain in the ASD group was also lower than that of the healthy group in Delta, Theta, Alpha, Beta band. Finally, combined with the WMSSE and ASI features of the F3/F4 channels (posterior frontal lobe) and F7/F8 channels (anterior temporal lobe), the classification accuracy and AUC value of ASD patients calculated by the SVM classification model were 82.7 ± 3.2%/ 0.795 (F3 / F4 channels), 89.8 ± 1.7%/ 0.812 (F7 / F8 channels). Comparison with existing methodsIt avoids the one-sided problem of single analysis complexity and synchronous connectivity, and provides a research basis for the comprehensive evaluation of ASD brain function. ConclusionWMSSE and ASI can be used as effective potential biomarkers for ASD diagnosis, and F7 and F8 channels can be preliminarily located as abnormal sensitive channels for ASD brain regulation. It also proves that the feature analysis of comprehensive complexity and synchronous connectivity is more conducive to the abnormal diagnosis of ASD patients.

Phase and Amplitude Synchronization in Power-Grid Frequency Fluctuations in the Nordic Grid

Monitoring and modelling the power grid frequency is key to ensuring stability in the electrical power system. Many tools exist to investigate the detailed deterministic dynamics and especially the bulk behaviour of the frequency. However, far less attention has been paid to its stochastic properties, and there is a need for a cohesive framework that couples both short-time scale fluctuations and bulk behaviour. Moreover, commonly assumed uncorrelated stochastic noise is predominantly employed in modelling in energy systems. In this publication, we examine the stochastic properties of the Nordic Grid, focusing on the increments of the frequency recordings. We show that these increments follow non-Gaussian statistics and display spatial and temporal correlations. Furthermore, we report two different physical synchronisation phenomena: a very short timescale phase synchronisation (< 2 s) followed by a slightly larger timescale amplitude synchronisation (2 s–5 s). Overall, these results show that modelling of fluctuations in power systems should not be restricted to Gaussian white noise.

Fast Synchronization Method of Comb-Actuated MEMS Mirror Pair for LiDAR Application.

MEMS-based LiDAR (micro-electro–mechanical system based light detection and ranging), with a low cost and small volume, becomes a promising solution for the two-dimensional (2D) and three-dimensional (3D) optical imaging. A semi-coaxial MEMS LiDAR design, based on a synchronous MEMS mirror pair, was proposed in our early study. In this paper, we specifically reveal the synchronization method of the comb-actuated MEMS mirror pair, including the frequency, amplitude, and phase synchronization. The frequency sweeping and phase adjustment are simultaneously implemented to accelerate the MEMS mirror synchronization process. The experiment is set up and the entire synchronization process is completed within 5 s. Eventually, a one-beam MEMS LiDAR system with the synchronous MEMS mirror pair is set up and a LiDAR with a field of view (FOV) of 60°, angular resolution of 0.2°, and frame rate of 360 Hz is obtained. The experimental results verify the feasibility of the MEMS mirror synchronization method and show a promising potential application prospect for the MEMS LiDAR system.

Connectivity of EEG synchronization networks increases for Parkinson\u2019s disease patients with freezing of gait

Freezing of gait (FoG), a paroxysmal gait disturbance commonly experienced by patients with Parkinson’s disease (PD), is characterized by sudden episodes of inability to generate effective forward stepping. Recent studies have shown an increase in beta frequency of local-field potentials in the basal-ganglia during FoG, however, comprehensive research on the synchronization between different brain locations and frequency bands in PD patients is scarce. Here, by developing tools based on network science and non-linear dynamics, we analyze synchronization networks of electroencephalography (EEG) brain waves of three PD patient groups with different FoG severity. We find higher EEG amplitude synchronization (stronger network links) between different brain locations as PD and FoG severity increase. These results are consistent across frequency bands (theta, alpha, beta, gamma) and independent of the specific motor task (walking, still standing, hand tapping) suggesting that an increase in severity of PD and FoG is associated with stronger EEG networks over a broad range of brain frequencies. This observation of a direct relationship of PD/FoG severity with overall EEG synchronization together with our proposed EEG synchronization network approach may be used for evaluating FoG propensity and help to gain further insight into PD and the pathophysiology leading to FoG.

Low-order modeling of the mutual synchronization between two turbulent thermoacoustic oscillators.

We use a low-order oscillator model to investigate the mutual synchronization of a thermoacoustic system consisting of two turbulent lean-premixed combustors coupled via a cross-talk tube. The model consists of two Van der Pol (VDP) oscillators coupled via dissipative and time-delay terms. We show that, despite its simplicity, the model can reproduce many of the synchronization phenomena observed experimentally, such as amplitude death, desynchronization (quasiperiodicity), synchronization (phase locking), and nonlinear energy pumping from a limit-cycle mode to a damped mode. This study shows that the mutual synchronization dynamics of a turbulent thermoacoustic system can be reproduced with just a simple coupled VDP model. This suggests that such a model could be used to identify new strategies for quenching limit-cycle oscillations in turbulent thermoacoustic systems, such as gas turbines and rocket engines.

Slow oscillations open susceptible time windows for epileptic discharges.

ObjectiveIn patients with epilepsy, interictal epileptic discharges are a diagnostic hallmark of epilepsy and represent abnormal, so‐called “irritative” activity that disrupts normal cognitive functions. Despite their clinical relevance, their mechanisms of generation remain poorly understood. It is assumed that brain activity switches abruptly, unpredictably, and supposedly randomly to these epileptic transients. We aim to study the period preceding these epileptic discharges, to extract potential proepileptogenic mechanisms supporting their expression.MethodsWe used multisite intracortical recordings from patients who underwent intracranial monitoring for refractory epilepsy, the majority of whom had a mesial temporal lobe seizure onset zone. Our objective was to evaluate the existence of proepileptogenic windows before interictal epileptic discharges. We tested whether the amplitude and phase synchronization of slow oscillations (.5–4 Hz and 4–7 Hz) increase before epileptic discharges and whether the latter are phase‐locked to slow oscillations. Then, we tested whether the phase‐locking of neuronal activity (assessed by high‐gamma activity, 60–160 Hz) to slow oscillations increases before epileptic discharges to provide a potential mechanism linking slow oscillations to interictal activities.ResultsChanges in widespread slow oscillations anticipate upcoming epileptic discharges. The network extends beyond the irritative zone, but the increase in amplitude and phase synchronization is rather specific to the irritative zone. In contrast, epileptic discharges are phase‐locked to widespread slow oscillations and the degree of phase‐locking tends to be higher outside the irritative zone. Then, within the irritative zone only, we observe an increased coupling between slow oscillations and neuronal discharges before epileptic discharges.SignificanceOur results show that epileptic discharges occur during vulnerable time windows set up by a specific phase of slow oscillations. The specificity of these permissive windows is further reinforced by the increased coupling of neuronal activity to slow oscillations. These findings contribute to our understanding of epilepsy as a distributed oscillopathy and open avenues for future neuromodulation strategies aiming at disrupting proepileptic mechanisms.

Brain network features based on theta-gamma cross-frequency coupling connections in EEG for emotion recognition

Emotion recognition is a hot topic in the field of cognitive neuroscience and interpersonal interaction, and EEG feature selection is an important classification technology. At present, the mainstream method of EEG feature selection is to extract non-interactive features of channels such as power spectral density, or correlation features among local multi-channels. With the application of complex network graph theory, the connection network between multiple brain regions is gradually included in feature selection. However, in the process of brain network construction, most of the current connections adopt simple signal phase or amplitude synchronization. In recent years, it has been found that in the process of emotion, memory, learning, and other advanced cognitive processes, the large-scale connection and communication between the brain regions are mainly completed by the cross-frequency coupling(CFC) between the low-frequency phase and the high-frequency amplitude of neural oscillations. Based on this, we use CFC to update the connection mode, reconstruct the brain network, and extract features for emotion recognition research. Our results show that the EEG network based on CFC performs better than other EEG synchronization networks in emotion classification. Moreover, the combination of global features and local features of the brain network, as well as the dynamic network features with continuous time-windows, can effectively improve the accuracy of emotion recognition. This study provides a new idea of network connection for the follow-up study of emotion recognition and other advanced cognitive activities and makes a pioneering exploration for further research on feature selection of emotion recognition and related neural circuits at the brain network level of functional connectivity.

Phase/Amplitude Synchronization of Brain Signals During Motor Imagery BCI Tasks.

In the last decade, functional connectivity (FC) has been increasingly adopted based on its ability to capture statistical dependencies between multivariate brain signals. However, the role of FC in the context of brain-computer interface applications is still poorly understood. To address this gap in knowledge, we considered a group of 20 healthy subjects during an EEG-based hand motor imagery (MI) task. We studied two well-established FC estimators, i.e. spectral- and imaginary-coherence, and we investigated how they were modulated by the MI task. We characterized the resulting FC networks by extracting the strength of connectivity of each EEG sensor and we compared the discriminant power with respect to standard power spectrum features. At the group level, results showed that while spectral-coherence based network features were increasing in the sensorimotor areas, those based on imaginary-coherence were significantly decreasing. We demonstrated that this opposite, but complementary, behavior was respectively determined by the increase in amplitude and phase synchronization between the brain signals. At the individual level, we eventually assessed the potential of these network connectivity features in a simple off-line classification scenario. Taken together, our results provide fresh insights into the oscillatory mechanisms subserving brain network changes during MI and offer new perspectives to improve BCI performance.

Benchmarking metrics for inferring functional connectivity from multi-channel EEG and MEG: A simulation study.

I present a systematic evaluation of different types of metrics, for inferring magnitude, amplitude, or phase synchronization from the electroencephalogram (EEG) and the magnetoencephalogram (MEG). I used a biophysical model, generating EEG/MEG-like signals, together with a system of two coupled self-sustained chaotic oscillators, containing clear transitions from phase to amplitude synchronization solely modulated by coupling strength. Specifically, I compared metrics according to five benchmarks for assessing different types of reliability factors, including immunity to spatial leakage, test-retest reliability, and sensitivity to noise, coupling strength, and synchronization transition. My results delineate the heterogeneous reliability of widely used connectivity metrics, including two magnitude synchronization metrics [coherence (Coh) and imaginary part of coherence (ImCoh)], two amplitude synchronization metrics [amplitude envelope correlation (AEC) and corrected amplitude envelope correlation (AECc)], and three phase synchronization metrics [phase coherence (PCoh), phase lag index (PLI), and weighted PLI (wPLI)]. First, the Coh, AEC, and PCoh were prone to create spurious connections caused by spatial leakage. Therefore, they are not recommended to be applied to real EEG/MEG data. The ImCoh, AECc, PLI, and wPLI were less affected by spatial leakage. The PLI and wPLI showed the highest immunity to spatial leakage. Second, the PLI and wPLI showed higher test-retest reliability and higher sensitivity to coupling strength and synchronization transition than the ImCoh and AECc. Third, the AECc was less noisy than the ImCoh, PLI, and wPLI. In sum, my work shows that the choice of connectivity metric should be determined after a comprehensive consideration of the aforementioned five reliability factors.

Synchronization of Fractional Order Neurons in Presence of Noise.

The firing rate of some biological neurons such as neocortical pyramidal neurons is consistent with fractional order derivative, and the fractional-order neuron models depict the firing rate of neurons more accurately than other integer order neuron models do. For this reason, first, the dynamical characteristics of fractional order Hindmarsh Rose (HR) neuron are investigated, here and then a two coupled neuronal system based on Hindmarsh Rose neuron is presented. The results show several differences in the dynamical cha.racteristics of integer order and fractional order Hindmarsh Rose neuron model. The integer order model shows only one type of firing characteristics when the parameter of the model remained the same. The fractional-order model depicts several dynamical behaviors even for the same parameters as the order of the fractional operator is varied with the same parameter values. The firing frequency increases as the order of the fractional operator decreases. The fractional-order is therefore key in determining the firing characteristics of biological neuron models. A linearized model of HR neuron is also given for hardware resource minimizations and to implement this neuronal network on a large scale. A synchronized system of two fractional-order fractional Hindmarsh-Rose (HR) neurons in the presence of noise is also presented. The dynamical characteristics of the modified coupled neuron are determined by the parameters of the neuron model and the coupling function. The robustness of the network in the presence of noise is verified by both amplitude and phase synchronization techniques. A simplification of the coupling function is also presented to reduce the hardware cost. The synchronization results show that the model can produce the desired behavior with acceptable error.