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## doi:10.1155/2012/239210 Review Article Inferring Functional Neural Connectivity with Phase Synchronization Analysis: A Review of Methodology

### Citations

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Citation Context ...s but neglects the effect of their amplitude. PSI has been demonstrated to be effective in inferring neural connectivity, especially when the connectivity is too weak to be detected by other measures =-=[8, 14]-=-. Note that there are other types of synchronization, such as complete synchronization and generalized synchronization [14, 15].Butmostofthemare defined for theoretical models of coupled oscillators a... |

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Citation Context ...narrower close to delta function (i.e., δ( f − fn)) in the frequency domain, the IF (1/2π)(dφ (b) (t)/dt) of the components in the pass band approaches the nominal frequency fn in an asymptotic sense =-=[46]-=-. Generally, to infer functional connectivity with PS analysis, we would recommend to define IP by combining the Hilbert transform with specific bandpass filter; that is, a bandpass filter is first ap... |

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Citation Context ...egions hold the property of criticality [20]. PSI, also called phase-locking value in literature, is proposed to quantify the level of PS and has been applied to a wide range of neuroscience research =-=[3, 5]-=-. For example, PSI has been used to examine the alternation of cortical connectivity prior to seizures [21] and neuronal synchrony after ischemic stroke [22], to identify mental states in brain-comput... |

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Citation Context ...e inverse discrete Fourier transform of ˜S(k); that is, ˜s(n) = 1 N−1 ∑ ˜S(k)e N k=0 j2πkn/N , n = 0, 1, ..., N − 1, (19) where ˜S(k) =|S(k)|ejν(k), (20) with a uniform random sequence {ν(k)} N−1 k=0 =-=[57, 58]-=-. A (1 − α) × 100% level of significance corresponds to a probability α of a false rejection. A larger number of surrogate realizations could offer a greater power in discrimination [57]. In [28], 99 ... |

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Citation Context ...frequency band for a duration, the multivariate signals are called in PS accordingly. In this section, we will further introduce two extensions/variations of PS analysis, that is, the trial-based PSI =-=[85, 86]-=- and the partial PSI [87]. A trial-based PSI is proposed to examine the variation of IP difference between signal channels across trials under repeated stimulus [85, 86]. For a data set of K trials an... |

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Citation Context ...ivalent to the squared MPC-based PSI in population statistic [71]. 4.3. Influence of Volume Conduction. The activities of a single source within the brain can be observed by many sensors on the scalp =-=[72]-=-. This is usually referred as volume conduction. Then the PSI between signals measured by different sensors, especially by spatially adjacent sensors, may be a trivial artefact due to volume conductio... |

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Citation Context ...vity prior to seizures [21] and neuronal synchrony after ischemic stroke [22], to identify mental states in brain-computer interface [23, 24], to investigate cognitive dysfunctions of mental disorder =-=[25]-=-, and to gain new strategies for clinical treatment [22, 26]. However, to get a reliable estimation of PSI from observed neural signals is not so easy, especially when the signals are with a small num... |

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Citation Context ...e synchronization analysis to inferring functional connectivity from neural signals. 1. Introduction Segregation and integration are two fundamental organization principles of neural systems in brain =-=[1]-=-. The neural organization can be investigated with functional neural connectivity in both local and global brain regions. The connectivity in local regions reflects specialized functions of local cort... |

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Citation Context ...egyisbasedon artificial surrogate data. Surrogate methods usually produce artificial data by randomizing the concerned property but keeping as much as possible other properties of the original signal =-=[49, 57]-=-. Then whether the original signal possesses the concerned property could be tests with the artificial surrogate data. Various surrogate methods have been proposed [8, 57–61]. For example, surrogate m... |

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Citation Context ...nded with respect to time. PS is ubiquitous in both natural and man-made systems, such as neural oscillations [4, 16], coupled chaotic2 Computational and Mathematical Methods in Medicine oscillators =-=[17]-=-, chaotic laser arrays [18], and electrochemical oscillations [19]. In addition, two metrics of PS, that is, the phase-lock interval and the lability of global synchronization, hold power law probabil... |

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Citation Context ...function. Here Cij( f ) is real, which implies that volume conduction of multiple sources strongly affects the real part of the cross-spectrum between si(t)andsj(t)butdoesnotaffect the imaginary part =-=[75, 76]-=-. The complex coherency of si(t)andsj(t)isdefinedas ( ) f Ω ( f ) = [ Cii Cij ( f ) C ∗ jj ( ) f ] 1/2 . (31) In [75], the imaginary part of Ω( f ) is defined as a synchronization measure for si(t) an... |

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Citation Context ... ischemic stroke [22], to identify mental states in brain-computer interface [23, 24], to investigate cognitive dysfunctions of mental disorder [25], and to gain new strategies for clinical treatment =-=[22, 26]-=-. However, to get a reliable estimation of PSI from observed neural signals is not so easy, especially when the signals are with a small number of samples and/or contaminated by noise [10, 11, 27, 28]... |

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Citation Context ...eatment [22, 26]. However, to get a reliable estimation of PSI from observed neural signals is not so easy, especially when the signals are with a small number of samples and/or contaminated by noise =-=[10, 11, 27, 28]-=-. Note that, in literature, other measures, such as phase clustering index, used different definition of phase, which is not within the framework of IP [29, 30]. In this paper, we review the methodolo... |

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Citation Context ...function. Here Cij( f ) is real, which implies that volume conduction of multiple sources strongly affects the real part of the cross-spectrum between si(t)andsj(t)butdoesnotaffect the imaginary part =-=[75, 76]-=-. The complex coherency of si(t)andsj(t)isdefinedas ( ) f Ω ( f ) = [ Cii Cij ( f ) C ∗ jj ( ) f ] 1/2 . (31) In [75], the imaginary part of Ω( f ) is defined as a synchronization measure for si(t) an... |

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Citation Context ...etween them or due to the indirect interaction mediated by other units. To deal with this problem, a measure called partial PSI is generalized from PS analysis following the idea of partial coherence =-=[87, 91]-=-. Combined with the pairwise PSI, the partial PSI can be used to distinguish the direct and indirect interdependencies among interacted systems/units [87]. For asetoftimeseries{si(n)}, i = 1, 2, ..., ... |

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Citation Context ...mation Bias. Another question in PS analysis is how long a epoch of signals is enough to get a reliable quantification of neural connectivity? One microstate of EEG signals usually lasts 50 to 200 ms =-=[3, 9, 66]-=-. However, various durations (from 100 ms to 10 ms) of EEG signals have been used in examining functional connectivity [12, 24, 67, 68]. A comprehensive study has been performed regarding this issue b... |

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Citation Context ...analysis. 2. Definition of Instantaneous Phase Before estimating the level of PS, the IP of each signal should be defined (Figure 1). The most basic definition of IP is based on the Hilbert transform =-=[14, 17, 36]-=-, which can be directly applied to coherent signals (i.e., narrow band signals with one prominent spectral component). But, for noncoherent data such as raw neural signals, this IP definition may yiel... |

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Citation Context ...he influence of reference on EEG signals is a long-lasting problem in quantifying functional connectivity [78–80]. Various reference strategies, such as bipolar EEG [81], average common reference EEG =-=[82]-=-, and Laplacian EEG [73], have been proposed. However, the cautions on these reference strategies have been extensively reported as well [81, 83]. The influence of reference has been examined with bot... |

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Citation Context ...egions hold the property of criticality [20]. PSI, also called phase-locking value in literature, is proposed to quantify the level of PS and has been applied to a wide range of neuroscience research =-=[3, 5]-=-. For example, PSI has been used to examine the alternation of cortical connectivity prior to seizures [21] and neuronal synchrony after ischemic stroke [22], to identify mental states in brain-comput... |

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Citation Context ...longing to different families may have weak correlation to each other in inferring neural connectivity, which implies that they each could characterize interdependence of signals in different aspects =-=[13]-=-. Among these measures, PSI quantifies the relationship between instantaneous phases (IP, represents the rhythm of oscillation or signal wave) of coupled systems/brain units but neglects the effect of... |

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Citation Context ... from s(t) bya certain operation; that is, I[A(t)e jφ(t) ] = ˜H[s(t)]. Among various operators ˜H(·) proposed, the Hilbert transform H(·) is the only one that satisfies the following three conditions =-=[45]-=-. (i) The associated amplitude A(t) is continuous and differentiable. (ii) The IPs of signals s(t)andc · s(t) is the same; that is, the operator should possess the property ˜H[c·s(t)] = c · ˜H[s(t)], ... |

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Citation Context ..., PSI has been used to examine the alternation of cortical connectivity prior to seizures [21] and neuronal synchrony after ischemic stroke [22], to identify mental states in brain-computer interface =-=[23, 24]-=-, to investigate cognitive dysfunctions of mental disorder [25], and to gain new strategies for clinical treatment [22, 26]. However, to get a reliable estimation of PSI from observed neural signals i... |

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Citation Context ...mation Bias. Another question in PS analysis is how long a epoch of signals is enough to get a reliable quantification of neural connectivity? One microstate of EEG signals usually lasts 50 to 200 ms =-=[3, 9, 66]-=-. However, various durations (from 100 ms to 10 ms) of EEG signals have been used in examining functional connectivity [12, 24, 67, 68]. A comprehensive study has been performed regarding this issue b... |

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Citation Context ...the Ising model and the Kuramoto model) and brain networks at a broadband frequency. These results imply that the IP association among multiple units or brain regions hold the property of criticality =-=[20]-=-. PSI, also called phase-locking value in literature, is proposed to quantify the level of PS and has been applied to a wide range of neuroscience research [3, 5]. For example, PSI has been used to ex... |

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Citation Context ...s but neglects the effect of their amplitude. PSI has been demonstrated to be effective in inferring neural connectivity, especially when the connectivity is too weak to be detected by other measures =-=[8, 14]-=-. Note that there are other types of synchronization, such as complete synchronization and generalized synchronization [14, 15].Butmostofthemare defined for theoretical models of coupled oscillators a... |

22 |
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Citation Context ...cially when the connectivity is too weak to be detected by other measures [8, 14]. Note that there are other types of synchronization, such as complete synchronization and generalized synchronization =-=[14, 15]-=-.Butmostofthemare defined for theoretical models of coupled oscillators and difficult to be applied to neural signal analysis. The coupled systems/units are claimed to be in phase synchronization (PS)... |

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Citation Context ...an be unified into one framework which defines IP with specific filter applied to signals [32]. (2) PSI and its significance test. We will introduce two commonly used PSIs, which are based on entropy =-=[2, 33]-=- and circular statistics [34, 35], respectively. We will further introduce several strategies to provide significance test for the estimated PSI. (3) Practical problems in PS detection. The estimation... |

17 |
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Citation Context ...he estimated PSIs of original EEG signal pairs in each case. Gamma waves Beta waves Alpha waves Theta waves The wrapped θ, that is, Θ = θ(mod2π), obeys the wrapped normal distribution, Θ ∼ Ñ(0, σ2 θ )=-=[35, 64]-=-, ∞∑ 1 p(Θ) = √ e 2πσθ k=−∞ −(Θ+2kπ)2 /(2σ2 θ ). (23) For the MPC-based PSI, λ =|E[ejϕ]|, the effect of noise appears as ̂λ = e −(σ2 θ 1 +σ 2 θ 2 )/2 λ; (24) that is, the noise introduces a degrading ... |

16 |
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Citation Context ...e MPC-based PSI is E{λ} ≈ 1 √ , (27) N where N is the number of samples used for PSI estimation [43, 69]. This means that the MPC-based PSI λ is a positively biased estimators for finite sample sizes =-=[70]-=-. More samples used will result in a less biased PSI. Then even for the same duration of signals, signals observed with higher sampling rate will yield a better estimation of the MPC-based PSI than th... |

16 |
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Citation Context ...ween signals measured by different sensors, especially by spatially adjacent sensors, may be a trivial artefact due to volume conduction, but not a true interaction of the underlying brain activities =-=[73]-=-. There are two ways to tackle this problem. One way is to estimate the true sources of underlying brain activities with observed EEG/MEG signals using inverse method and then quantify the relationshi... |

15 |
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Citation Context ...ms/units are claimed to be in phase synchronization (PS) when the difference of IPs is bounded with respect to time. PS is ubiquitous in both natural and man-made systems, such as neural oscillations =-=[4, 16]-=-, coupled chaotic2 Computational and Mathematical Methods in Medicine oscillators [17], chaotic laser arrays [18], and electrochemical oscillations [19]. In addition, two metrics of PS, that is, the ... |

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Citation Context ...PS is ubiquitous in both natural and man-made systems, such as neural oscillations [4, 16], coupled chaotic2 Computational and Mathematical Methods in Medicine oscillators [17], chaotic laser arrays =-=[18]-=-, and electrochemical oscillations [19]. In addition, two metrics of PS, that is, the phase-lock interval and the lability of global synchronization, hold power law probability distributions for both ... |

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Citation Context ...ese components as well. Various measures, such as cross-correlation, coherence, nonlinear interdependence [10], mutual information [8], partial directed coherence [9], correlation-entropy coefficient =-=[92]-=-, and coherence entropy coefficient [13], have been proposed in functional connectivity analysis based on EEG, MEG signals and simulated data from various aspects [10– 13, 93–95]. Results show that th... |

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Citation Context ...ically meaningless [37–39]. One way is to process noncoherent signal with a specific narrow bandpass filter. An alternative way is to define IP based on other transforms such as the wavelet transform =-=[18, 19, 31, 40]-=-. PS detection based on these IP definitions has been compared numerically with both simulation data and experimental signals, yielding similar connectivity [10, 11]. In addition, an analytical study ... |

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Citation Context ...gnals and using independent white noise as the inputs to the model. The surrogate data generated by this method are linear stochastic processes and have the same power spectra of the original signals =-=[57, 60]-=-. In another study, a method named twin surrogate is proposed based on the recurrence properties. It is demonstrated to be suitable to provide significance test for PS in Rössler oscillators [61]. In ... |

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Citation Context ...〉 t tComputational and Mathematical Methods in Medicine 9 However, it has been demonstrated that the imaginary part of 〈Ω( f )〉 f is not a good index of PS as it depends on the amplitudes of signals =-=[76, 77]-=-. Further, a measure called phase lag index, 〈 η = ∣ sign [ φi(t) − φj(t) ]〉 ∣ ∣, (34) was proposed based on the consideration that “the existence of a consistent, nonzero phase lag between two times ... |

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Citation Context ...ms/units are claimed to be in phase synchronization (PS) when the difference of IPs is bounded with respect to time. PS is ubiquitous in both natural and man-made systems, such as neural oscillations =-=[4, 16]-=-, coupled chaotic2 Computational and Mathematical Methods in Medicine oscillators [17], chaotic laser arrays [18], and electrochemical oscillations [19]. In addition, two metrics of PS, that is, the ... |

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Citation Context ..., the multivariate signals are called in PS accordingly. In this section, we will further introduce two extensions/variations of PS analysis, that is, the trial-based PSI [85, 86] and the partial PSI =-=[87]-=-. A trial-based PSI is proposed to examine the variation of IP difference between signal channels across trials under repeated stimulus [85, 86]. For a data set of K trials and each trial with N sampl... |

10 |
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Citation Context ...eatment [22, 26]. However, to get a reliable estimation of PSI from observed neural signals is not so easy, especially when the signals are with a small number of samples and/or contaminated by noise =-=[10, 11, 27, 28]-=-. Note that, in literature, other measures, such as phase clustering index, used different definition of phase, which is not within the framework of IP [29, 30]. In this paper, we review the methodolo... |

10 |
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Citation Context ... to quantify the level of PS and has been applied to a wide range of neuroscience research [3, 5]. For example, PSI has been used to examine the alternation of cortical connectivity prior to seizures =-=[21]-=- and neuronal synchrony after ischemic stroke [22], to identify mental states in brain-computer interface [23, 24], to investigate cognitive dysfunctions of mental disorder [25], and to gain new strat... |

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Citation Context ... [57, 60]. In another study, a method named twin surrogate is proposed based on the recurrence properties. It is demonstrated to be suitable to provide significance test for PS in Rössler oscillators =-=[61]-=-. In [28], four different surrogate methods, which generate artificial surrogate data by shuffling the rank order, the phase spectra, the IP of original EEG signals, are compared in significance test ... |

10 |
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Citation Context ...s in short time window, so as to obtain functional connectivity with a certain degree of temporal resolution. Regarding this problem, a new measure called pairwise phase consistency has been proposed =-=[71]-=-. This measure is defined as the mean of the cosine of IP difference across all given signal pairs; that is, ξ = N−1 2 ∑ N(N − 1) i=1 N∑ k=i+1 cos ( ) φi − φk . (28) Pairwise phase consistency quantif... |

9 | 2004 Testing for phase synchronization
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Citation Context ...ndent on the number of edges, that is, the number of connectivity with significantly big strength. One way to decide the value of this common threshold is based on significance test for estimated PSI =-=[8, 34, 49, 56]-=-. Here we introduce three different strategies in providing significance threshold for PS analysis. 3.2.1. Artificial Surrogate Tests. Thefirststrategyisbasedon artificial surrogate data. Surrogate me... |

9 |
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Citation Context ...ncreases from 0 to ∞. In addition, a method based on independent component analysis has been demonstrated to be an appropriate method to generate reference for EEG signals in quantifying connectivity =-=[84]-=-. 5. Extensions of Phase Synchronization Analysis Various extensions of PS analysis have been proposed to infer the relationship in multivariate or multitrial signals based on the concept of IP [85–90... |

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Citation Context ...egers. In this paper, we focus on the case of 1 : 1 PS, which is defined based on samples of one trial in the time domain. Most conclusions for 1 : 1 PS can be easily extended to the case of p : q PS =-=[47, 48]-=-. In neuroscience research, the estimated PSI is usually taken as one kind of functional connectivity in neural signals. Here we introduce two PSIs which have been commonly used to quantify the functi... |

8 |
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Citation Context ...sis is suitable for neuroscience research, as we are usually interested in the relationship between neural oscillations in particular frequency bands such as beta waves ([12, 30] Hz) and gamma waves (=-=[30, 80]-=- Hz) rather than the interaction between broadband raw signals. While inferring functional neural connectivity with PS analysis, several cautions and limitations should be taken into consideration. Fi... |

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Citation Context ...eatment [22, 26]. However, to get a reliable estimation of PSI from observed neural signals is not so easy, especially when the signals are with a small number of samples and/or contaminated by noise =-=[10, 11, 27, 28]-=-. Note that, in literature, other measures, such as phase clustering index, used different definition of phase, which is not within the framework of IP [29, 30]. In this paper, we review the methodolo... |

7 |
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Citation Context ...th exact rhythm locking and PSI = 0 indicating no PS at all. Beside these two indexes, other measures, such as the index based on conditional probability [2] and the index based on mutual information =-=[49]-=-, have also been applied to the quantification of relationship between IPs. More discussions on PSI can be found in [8]. 3.2. Significance Tests for PSI. In inferring neural connectivity, a highly con... |

7 |
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Citation Context ...connectivity? One microstate of EEG signals usually lasts 50 to 200 ms [3, 9, 66]. However, various durations (from 100 ms to 10 ms) of EEG signals have been used in examining functional connectivity =-=[12, 24, 67, 68]-=-. A comprehensive study has been performed regarding this issue based on both surrogate tests and intersubject EEG surrogate test [28]. Results show that a duration of EEG waves of 3 ∼ 18 wave cycles ... |

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Citation Context ..., PSI has been used to examine the alternation of cortical connectivity prior to seizures [21] and neuronal synchrony after ischemic stroke [22], to identify mental states in brain-computer interface =-=[23, 24]-=-, to investigate cognitive dysfunctions of mental disorder [25], and to gain new strategies for clinical treatment [22, 26]. However, to get a reliable estimation of PSI from observed neural signals i... |

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Citation Context ...n-made systems, such as neural oscillations [4, 16], coupled chaotic2 Computational and Mathematical Methods in Medicine oscillators [17], chaotic laser arrays [18], and electrochemical oscillations =-=[19]-=-. In addition, two metrics of PS, that is, the phase-lock interval and the lability of global synchronization, hold power law probability distributions for both simulation systems (i.e., the Ising mod... |

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Citation Context ... which defines IP with specific filter applied to signals [32]. (2) PSI and its significance test. We will introduce two commonly used PSIs, which are based on entropy [2, 33] and circular statistics =-=[34, 35]-=-, respectively. We will further introduce several strategies to provide significance test for the estimated PSI. (3) Practical problems in PS detection. The estimation of PSI is affected by observatio... |

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Citation Context ...= s(t) ∗ g(t)e j2πfnt] = s (b) (t), (14) where F −1 (·) denotes the inverse Fourier transform operator. Beside IP definitions within this framework, there are IP definitions proposed in other aspects =-=[43, 44]-=-. For example, the IP and PSI based on Rihaczek distribution are more robust to noise than the method based on the wavelet transform [43]. 2.2. Constraints for IP Definition. For a real signal s(t) = ... |

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Citation Context ...forms, such as the Hilbert transform [17] and the wavelet transform [31]. But actually, these IP definitions can be unified into one framework which defines IP with specific filter applied to signals =-=[32]-=-. (2) PSI and its significance test. We will introduce two commonly used PSIs, which are based on entropy [2, 33] and circular statistics [34, 35], respectively. We will further introduce several stra... |

3 | Definitions of instantaneous frequency under physical constraints - Oliveira, Barroso - 2000 |

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H (2011) Adaptive phase extraction: Incorporating the Gabor transform in the matching pursuit algorithm
- Wacker, Witte
(Show Context)
Citation Context ...= s(t) ∗ g(t)e j2πfnt] = s (b) (t), (14) where F −1 (·) denotes the inverse Fourier transform operator. Beside IP definitions within this framework, there are IP definitions proposed in other aspects =-=[43, 44]-=-. For example, the IP and PSI based on Rihaczek distribution are more robust to noise than the method based on the wavelet transform [43]. 2.2. Constraints for IP Definition. For a real signal s(t) = ... |

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et al., “Dysfunctional long-range coordination of neural activity during gestalt perception in schizophrenia
- Uhlhaas, Linden, et al.
- 2006
(Show Context)
Citation Context ...connectivity? One microstate of EEG signals usually lasts 50 to 200 ms [3, 9, 66]. However, various durations (from 100 ms to 10 ms) of EEG signals have been used in examining functional connectivity =-=[12, 24, 67, 68]-=-. A comprehensive study has been performed regarding this issue based on both surrogate tests and intersubject EEG surrogate test [28]. Results show that a duration of EEG waves of 3 ∼ 18 wave cycles ... |

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The effect of a scalp reference signal on coherence measurements of intracranial electroencephalograms, Clin. Neurophysiol
- Zaveri, Duckrow, et al.
- 2000
(Show Context)
Citation Context ...es, such as bipolar EEG [81], average common reference EEG [82], and Laplacian EEG [73], have been proposed. However, the cautions on these reference strategies have been extensively reported as well =-=[81, 83]-=-. The influence of reference has been examined with both analytical analysis and computational simulation [68]. Let u(t) = Vr(t) denote the reference signal, where V > 0is coefficient and r(t) is time... |

2 |
Phase synchronization analysis of eeg signals: an evaluation based on surrogate tests
- Sun, Hong, et al.
- 2012
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Citation Context |

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da Silva F. Enhancement of phase clustering in the EEG/MEG gamma frequency band anticipates transitions to paroxismal epileptiform activity in epileptic patients with known visual sensitivity
- Kalitzin, Parra, et al.
(Show Context)
Citation Context ...es and/or contaminated by noise [10, 11, 27, 28]. Note that, in literature, other measures, such as phase clustering index, used different definition of phase, which is not within the framework of IP =-=[29, 30]-=-. In this paper, we review the methodology of PS analysis in inferring functional neural connectivity from the following aspects. (1) IP definition. To detect PS in a pair of signals, various IP defin... |

2 | Phase and average period of chaotic oscillators - Pereira, Baptista, et al. - 2007 |

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On the use of bipolar montages for time-series analysis of intracranial electroencephalograms
- ZAVERI, DUCKROW, et al.
- 2006
(Show Context)
Citation Context ...70]. 4.4. Influence of Reference. The influence of reference on EEG signals is a long-lasting problem in quantifying functional connectivity [78–80]. Various reference strategies, such as bipolar EEG =-=[81]-=-, average common reference EEG [82], and Laplacian EEG [73], have been proposed. However, the cautions on these reference strategies have been extensively reported as well [81, 83]. The influence of r... |

2 | Visual working memory loadrelated changes in neural activity and functional connectivity
- Li, Zhang, et al.
- 2011
(Show Context)
Citation Context ...frequency band for a duration, the multivariate signals are called in PS accordingly. In this section, we will further introduce two extensions/variations of PS analysis, that is, the trial-based PSI =-=[85, 86]-=- and the partial PSI [87]. A trial-based PSI is proposed to examine the variation of IP difference between signal channels across trials under repeated stimulus [85, 86]. For a data set of K trials an... |

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et al: Frequency flows and the time-frequency dynamics of multivariate phase synchronization in brain signals
- Rudrauf
(Show Context)
Citation Context ... multivariate or multitrial signals based on the concept of IP [85–90]. For example, a method named frequency flow analysis has been used to examine the global synchronization of multivariate signals =-=[88]-=-. If the IF, derived from IP, of each variable almost equals to the IFs of other variables in a certain frequency band for a duration, the multivariate signals are called in PS accordingly. In this se... |

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De Vico Fallani, F. Cincotti et al., “Estimation of effective and functional cortical connectivity from neuroelectric and hemodynamic recordings
- Astolfi, F
- 2009
(Show Context)
Citation Context ...connectivity? One microstate of EEG signals usually lasts 50 to 200 ms [3, 9, 66]. However, various durations (from 100 ms to 10 ms) of EEG signals have been used in examining functional connectivity =-=[12, 24, 67, 68]-=-. A comprehensive study has been performed regarding this issue based on both surrogate tests and intersubject EEG surrogate test [28]. Results show that a duration of EEG waves of 3 ∼ 18 wave cycles ... |

1 |
An approach to chaotic synchronization
- Hramov, Koronovskii
- 2004
(Show Context)
Citation Context ...etect PS in a pair of signals, various IP definitions have been proposed. Most of these IP definitions are based on particular transforms, such as the Hilbert transform [17] and the wavelet transform =-=[31]-=-. But actually, these IP definitions can be unified into one framework which defines IP with specific filter applied to signals [32]. (2) PSI and its significance test. We will introduce two commonly ... |

1 | Spurious detection of phase synchronization in coupled nonlinear oscillators - Xu, Chen, et al. - 2006 |

1 | Spectrographic measurement of instantaneous frequency and the time-dependent weighted average instantaneous frequency - Loughlin - 1999 |

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Computer measuring of frequency stability and the analytic signal
- Vakman
- 1994
(Show Context)
Citation Context ...nominal frequency fn, and response duration T. The filter assures that the extracted signal wave is coherent. s (b)(t) is analytic in an asymptotic sense as the bandwidth of b(t) is smaller than 2 fn =-=[36, 41, 42]-=-. This method is exactly the one based on a Gaussian filter when the envelope g(t) is a Gaussian function. Filter b(t) canbe expressed as B ( f ) ∫ ∞ = b(t)e −∞ −j2πftdt = G ( ) f − fn (12) in the fre... |

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On the stability of the n:m phase synchronization index
- Wacker, Witte
- 2011
(Show Context)
Citation Context ...egers. In this paper, we focus on the case of 1 : 1 PS, which is defined based on samples of one trial in the time domain. Most conclusions for 1 : 1 PS can be easily extended to the case of p : q PS =-=[47, 48]-=-. In neuroscience research, the estimated PSI is usually taken as one kind of functional connectivity in neural signals. Here we introduce two PSIs which have been commonly used to quantify the functi... |

1 | Reorganization of brain networks in aging and age-related diseases,” Aging and Disease - Sun, Tong, et al. |

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Thiel et al., “Synchronization analysis of coupled noncoherent oscillators
- Kurths, Romano, et al.
- 2006
(Show Context)
Citation Context ...e effect of volume conduction, and the influence of reference in PS analysis. 4.1. Effect of Noise in PS Detection. The effect of noise in PS detection has been examined by both numerical computation =-=[10, 11, 27, 33, 62, 63]-=- and analytical study [32]. A bandpass prefiltering can suppress the effect of noise but may introduce spurious connectivity as well [33]. In this section, we mainly review a theoretical study on the ... |

1 |
Detecting phase synchronization in noisy data from coupled chaotic oscillators
- Sun, Zhang, et al.
- 2008
(Show Context)
Citation Context ...e effect of volume conduction, and the influence of reference in PS analysis. 4.1. Effect of Noise in PS Detection. The effect of noise in PS detection has been examined by both numerical computation =-=[10, 11, 27, 33, 62, 63]-=- and analytical study [32]. A bandpass prefiltering can suppress the effect of noise but may introduce spurious connectivity as well [33]. In this section, we mainly review a theoretical study on the ... |

1 |
Characterizing and approximating infinite scale mixtures of normals
- Hamdan
- 2006
(Show Context)
Citation Context ...own, the empirical distribution of IP error {θ(n)} can be approximated as K∑ pm(θ) = p(θ | σk)πk, (26) k=1 where {πk} K k=1 are the respective empirical probabilities which are estimated from {Ax(n)} =-=[65]-=-. Note that Ax(n) is the instantaneous amplitude of the clean signal, and thus it is difficult to obtain its distribution with only the observed noisy signal {s(n)}. Simulations are performed by consi... |

1 | Coherence and phase synchrony analysis of electroencephalogram
- Tcheslavski
- 2005
(Show Context)
Citation Context ...th no synchrony is assumed to obey uniform distribution. Under this assumption, the expected value of the MPC-based PSI is E{λ} ≈ 1 √ , (27) N where N is the number of samples used for PSI estimation =-=[43, 69]-=-. This means that the MPC-based PSI λ is a positively biased estimators for finite sample sizes [70]. More samples used will result in a less biased PSI. Then even for the same duration of signals, si... |

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The volume conductor may act asatemporalfilterontheecgandEEG,”Medical
- Stinstra, Peters
- 1998
(Show Context)
Citation Context ... two signals si(t) and sj(t) collected by sensors i and j are from a linear superposition of K independent sources xk(t), and the mapping of each source to sensors is instantaneous with no distortion =-=[74]-=-. Then in the frequency domain, si(t) canbe expressed as ( ) Si f = K∑ ( ) aikXk f , (29) k=1 where Si( f )andXk( f ) are the Fourier transform of si(t)and xk(t), respectively, and aik are the contrib... |

1 | Dangerous phase,” Neuroinformatics,vol.3,no.4 - Schiff - 2005 |

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Bergmans et al., “An investigation of the phase locking index for measuring of interdependency of cortical source signals recorded in the EEG
- Sazonov, Ho, et al.
- 2009
(Show Context)
Citation Context ...5]. Results show that they can reveal a similar tendency of global connectivity [10]. The MPC-based PSI has been argued to be slightly better than coherence for both estimation and detection purposes =-=[93]-=-. In another study, total 34 different measures are classified into several families such as correlation/coherence family, mutual information family, PS family, and the Granger causality family. These... |