Spatiotemporal dynamics of maximal and minimal EEG spectral power

Oscillatory neural activities are prevalent in the brain with their phase realignment contributing to the coordination of neural communication. Phase realignments may have especially strong (or weak) impact when neural activities are strongly synchronized (or desynchronized) within the interacting populations. We report that the spatiotemporal dynamics of strong regional synchronization measured as maximal EEG spectral power—referred to as activation—and strong regional desynchronization measured as minimal EEG spectral power—referred to as suppression—are characterized by the spatial segregation of small-scale and large-scale networks. Specifically, small-scale spectral-power activations and suppressions involving only 2–7% (1–4 of 60) of EEG scalp sites were prolonged (relative to stochastic dynamics) and consistently co-localized in a frequency specific manner. For example, the small-scale networks for θ, α, β1, and β2 bands (4–30 Hz) consistently included frontal sites when the eyes were closed, whereas the small-scale network for γ band (31–55 Hz) consistently clustered in medial-central-posterior sites whether the eyes were open or closed. Large-scale activations and suppressions involving over 17–30% (10–18 of 60) of EEG sites were also prolonged and generally clustered in regions complementary to where small-scale activations and suppressions clustered. In contrast, intermediate-scale activations and suppressions (involving 7–17% of EEG sites) tended to follow stochastic dynamics and were less consistently localized. These results suggest that strong synchronizations and desynchronizations tend to occur in small-scale and large-scale networks that are spatially segregated and frequency specific. These synchronization networks may broadly segregate the relatively independent and highly cooperative oscillatory processes while phase realignments fine-tune the network configurations based on behavioral demands.


Introduction
Many studies have investigated macroscopic networks of oscillatory neural activity in humans by examining the spatiotemporal patterns of spectral amplitude, phase, and phaseamplitude relations within and across frequency bands and brain regions using EEG and MEG methods. Those studies typically examined oscillatory interactions in specific regions of interest or characterized networks of oscillatory activities and their connectivity by analyzing the structures of correlation matrices (derived from pairwise temporal associations of spectral amplitude and/or phase across space and/or frequencies), often utilizing clustering methods and/or graph theoretic measures derived from correlation matrices [1-9;; see 10 for a review].
EEG recorded at each scalp electrode is thought to reflect the macroscopically summed field potentials arising from the current sources/sinks generated by the regional population of large cortical pyramidal cells that are aligned in parallel and perpendicular to the cortical surface [e.g., 28]. Thus, it is reasonable to infer that larger spectral power at a scalp site reflects more extensive oscillatory synchronization within the accessible regional pyramidal-cell population (resulting in less cancellation of field oscillations), whereas smaller spectral power reflects less extensive oscillatory synchronization which may result from less cells being engaged in oscillatory activity and/or desynchronization of oscillations (resulting in greater cancellation of field oscillations). Thus, spectral power at each scalp electrode reflects the degree of oscillatory synchronization of the regional population of the contributing cortical pyramidal cells (though non-oscillatory components and some artifacts may also contribute to spectral power;; see Caveats). Our spatial resolution was 1-2 cm after surface-Laplacian transforming the scalprecorded EEG to infer the macroscopic current source/sink densities at the electrode sites (see Materials and methods).
Phenomenologically, we became intrigued by the observation that spectral power sometimes spontaneously maximized or minimized in isolation exclusively at a single site, whereas at other times, spectral power globally maximized or minimized over a large number of sites. For convenience, we refer to maximal spectral power (defined by an upper percentile threshold;; see Results and discussion) as activation in the sense of activation of extensive regional oscillatory synchronization, and minimal spectral power (defined by a lower percentile threshold) as suppression in the sense of suppression of regional oscillatory synchronization.
Are there general rules governing the spontaneous fluctuations in the spatial extent and clustering of spectral-power activations and suppressions? Our strategy was to examine the number of concurrently activated or suppressed sites as a function of time. In particular, we determined whether consistent spatial patterns of activations and suppressions emerged as a function of the number of concurrently activated or suppressed sites. For example, if a specific group of n sites formed a network, that is, if a specific group of n sites tended to be concurrently activated or suppressed, whenever the number of concurrently activated or suppressed sites happened to be n, a specific group of sites should be consistently included with elevated probability.
This approach may appear similar to finding clusters in a correlation matrix (e.g., constructed from binarized values, +1 for activation and -1 for suppression), but there are some crucial differences. First, the current method allows direct examinations of the spatial consistency and temporal dynamics of the clusters of activations and suppressions of different sizes that actually occur (rather than inferring time-averaged clusters from correlation matrices by using cluster number as a fitting parameter). For instance, suppose activations at site A were variously correlated with activations at other sites, but rare isolated activations consistently occurred at site A. Analyses of correlation matrices would miss it (because pairwise correlations do not track instantaneous spatial patterns), but the current analysis would detect it. The current analysis would also reveal the dynamics (e.g., average duration) of such rare but consistently isolated activations occurring at site A. Second, the current method allows examinations of how temporal contexts influence the clustering of activations and suppressions. For instance, the composition of a small cluster of activations may differ depending on whether it occurs in the midst of a persisting period of small-cluster activations, immediately following a period of widespread activations, or immediately preceding the emergence of widespread activations.
Information about temporal contexts is unavailable in correlation matrices. Overall, the current analysis is complementary to structural analyses applied to correlation matrices.
To increase the generalizability of our results, we examined spontaneous spatiotemporal fluctuations in spectral-power activations and suppressions while participants rested with their eyes closed, rested with their eyes open in a dark room, or casually viewed a silent nature video.
The results provided converging evidence suggesting that the spatiotemporal dynamics of spectral-power activations and suppressions are characterized by the spatial segregation of small-scale and large-scale networks. Specifically, small-scale spectral-power activations and suppressions involving only 2-7% (1-4 of 60) of EEG scalp sites were prolonged (relative to stochastic dynamics), consistently co-localized in a frequency specific manner, and were stable while the spatial extent of activations/suppressions remained in the small-scale range. Largescale activations and suppressions involving over 17-30% (over 10-18 of 60) of EEG sites were also prolonged, generally clustered in regions complementary to where small-scale activations and suppressions clustered, and were stable while the spatial extent of activations/suppressions remained in the large-scale range. These macroscopic networks of strong synchronization and desynchronization may broadly segregate the relatively independent and highly cooperative oscillatory processes while phase realignments may fine-tune the network configurations based on behavioral demands.

Participants
Fifty-two Northwestern University students (35 women, 1 non-binary who declined to identify their gender as either woman or man;; mean age of 20.8 years, ranging from 18 to 29 years, standard deviation of 2.5 years) signed a written consent form to participate for monetary compensation ($10/hr). All were right-handed, had normal hearing and normal or corrected-tonormal vision, and had no history of concussion. They were tested individually in a dimly lit or dark room. The study protocol was approved by the Northwestern University Institutional Review Board. Participants p1-p7 and p12-p28 (N = 24) participated in a rest-with-eyes-closed condition in which EEG was recorded for ~5 min while participants rested with their eyes closed and freely engaged in spontaneous thoughts. Participants p8-p28 (N = 21) subsequently participated in a silent-nature-video condition in which EEG was recorded for ~5 min while they viewed a silent nature video. To evaluate test-retest reliability, the silent-nature-video condition was run twice (20-30 min apart), labeled as earlier viewing and later viewing in the analyses. A generic nature video was presented on a 13-inch, 2017 MacBook Pro, 2880(H)-by-1800(V)pixel-resolution LCD monitor with normal brightness and contrast settings, placed 100 cm away from participants, subtending approximately 16°(H)-by-10°(V) of visual angle. Participants p29-p52 (N = 24) participated in the replication of the rest-with-eyes-closed condition and subsequently participated in a rest-with-eyes-open-in-dark condition which was the same as the former except that the room was darkened and participants kept their eyes open while blinking naturally. Subsets of these EEG data were previously analyzed for a different purpose [29][30][31].

EEG recording and pre-processing
While participants rested with their eyes closed, rested with their eyes open in dark, or viewed a silent nature video for approximately 5 min, EEG was recorded from 64 scalp electrodes (although we used a 64-electrode montage, we excluded signals from noise-prone electrodes, Fpz, Iz, T9, and T10, from analyses) at a sampling rate of 512 Hz using a BioSemi ActiveTwo system (see www.biosemi.com for details). Electrooculographic (EOG) activity was monitored using four face electrodes, one placed lateral to each eye and one placed beneath each eye. Two additional electrodes were placed on the left and right mastoid area. The EEG data were preprocessed using EEGLAB and ERPLAB toolboxes for MATLAB [31][32]. The data were re-referenced offline to the average of the two mastoid electrodes, bandpass-filtered at 0.01 Hz-80 Hz, and notch-filtered at 60 Hz (to remove power-line noise that affected the EEG signals from some participants). For the EEG signals recorded while participants rested with the eyes open in dark or while they viewed a silent nature video, an Independent Component Analysis (ICA) was conducted using EEGLABs' runica function [33][34]. Blink related components were visually identified (apparent based on characteristic topography) and removed (no more than two components were removed per participant).
We surface-Laplacian transformed all EEG data for the following reasons. The transform (1) substantially reduces volume conduction (reducing the electrode-distance dependent component of phase alignment to within adjacent sites, or 1-2 cm, for a 64-channel montage [35]), (2) virtually eliminates the effects of reference electrode choices (theoretically;; we also verified this for our data), and (3) provides a data-driven method to fairly accurately map scalprecorded EEG to macroscopic current-source/sink densities over the cortical surface [36][37][38].
We used Perrin and colleagues' algorithm [39][40][41] with the "smoothness" value, l = 10 -5 (recommended for 64 channels [35]). We refer to the surface-Laplacian transformed EEG signals that represent the macroscopic current source/sink densities under the 60 scalp sites (with the 4 noise-prone sites removed from analyses;; see above) simply as EEG signals. These EEG-recording and pre-processing procedures were identical to those used in our prior study [29].

EEG analysis
We used the temporal derivative of EEG as in our prior studies that examined all [29] or a subset [31] of the current EEG data for different purposes. While the rationale for taking the temporal derivative of EEG is detailed in [29], it offers the following advantages. First, EEG temporal derivatives may highlight oscillatory dynamics by reducing the non-oscillatory 1/f b spectral backgrounds when b~1, which was the case for our EEG data on the timescale of several seconds [29]. Second, EEG temporal derivatives may be considered a "deeper" measure of neural activity than EEG in the sense that scalp-recorded potentials are caused by the underlying neural currents and taking EEG temporal derivative macroscopically estimates those currents (as currents in RC circuits are proportional to the temporal derivative of the corresponding potentials). Third, EEG temporal derivatives are drift free. Prior studies used EEG temporal derivatives for similar reasons [e.g., [42][43][44], providing some evidence suggesting that EEG temporal derivatives yield more effective neural features than EEG for brain-computer interface [44].
We generated phase-scrambled controls whose spectral power fluctuated stochastically while maintaining the time-averaged spectral-amplitude profiles of the actual EEG data. While phase-scrambling can be performed using several different methods, we chose discrete cosine transform, DCT [45]. In short, we transformed each ~5 min EEG waveform with type-2 DCT, randomly shuffled the signs of the coefficients, and then inverse-transformed it with type-3 DCT (the "inverse DCT"), which yielded a phase-scrambled version. DCT phase-scrambling is similar to DFT (discrete Fourier transform) phase-scrambling except that it is less susceptible to edge effects. We previously verified that DCT phase-scrambling generated waveforms whose spectral-power fluctuations conformed to exponential distributions [29, Fig  2] indicative of a Poisson point process (an unpredictable and memory-free process), with negligible distortions to the time-averaged spectral-amplitude profiles of the actual EEG data [29, Fig  1].
To investigate how spectral power (amplitude squared of sinusoidal components) fluctuated over time, we used a Morlet wavelet-convolution method suitable for time-frequency decomposition of signals containing multiple oscillatory sources of different frequencies (see [35] for a review of different methods for time-frequency decomposition). Each Morlet wavelet is a Gaussian-windowed sinusoidal templet characterized by its center frequency as well as its temporal and spectral widths that limit its temporal and spectral resolution. We decomposed each EEG waveform (i.e., its temporal derivative) into a time series of spectral power using Morlet wavelets with 200 center frequencies, f c 's, between 3 Hz and 60 Hz. The f c 's were logarithmically spaced because neural temporal-frequency tunings tend to be approximately logarithmically scaled [46][47]. The accompanying n factors (roughly the number of cycles per wavelet, = 2 • , where SD is the wavelet standard deviation) were also logarithmically spaced between 3 and 16, yielding temporal resolutions ranging from SD = 159 ms (at 3 Hz) to

Results and discussion
Setting thresholds to define maximal and minimal spectral power The goal of this study was to uncover rules (if any) that govern the spatiotemporal dynamics of maximal and minimal spectral power. To this end, we first operationalized maximal and minimal spectral power as the top-i th -percentile and the bottom-j th -percentile spectral power, which we refer to as activation and suppression (see Introduction).
The number of concurrently activated/suppressed sites dynamically increases and decreases, making the spatial extent of spectral-power activations/suppressions dynamically expand and contract. In this context, focal activations/suppressions occurring exclusively at single sites are special in that they may reflect the instances of relatively independent controls of activation/suppression. Thus, as a first step, we calibrated activation and suppression thresholds so that the instances of focal activation and focal suppression were detected with maximal sensitivity. Specifically, we determined the percentile thresholds (applied per scalp site per frequency band per condition per participant) that maximized the prevalence of focal activations and suppressions relative to chance levels.
For a broad range of thresholds, the instances of focal activations (the upper row in Fig  1) and focal suppressions (the lower row in Fig  1) were elevated relative to the corresponding Binomial probabilities given by 60 • 1 − ./01 , where p is the percentile threshold and 60 is the number of sites. Notably, the 8 th -percentile threshold clearly maximized the instances of both focal activations and suppressions for all frequency bands across all conditions (Fig  1). We thus defined activation as yielding the top-8 th -percentile spectral power and suppression as yielding the bottom-8 th -percentile spectral power (per scalp site per frequency band per condition per participant). As expected, all phase-scrambled controls conformed to the Binomial probabilities (not shown, but they would yield straight horizontal lines at y = 0 in Fig  1).

Dynamics of the spatial scale of spectral-power activations and suppressions
To examine the dynamics of the spatial scale of spectral-power activations and suppressions, we examined the time series of the number of activated or suppressed sites, for the actual data (Fig  2A) than for the phase-scrambled control ( Fig  2B). Though less apparent, one can also see that the typical durations of small-scale activations (the red highlighted portions below n sites = 4) were longer for the actual data (Fig  2A) than for the phasescrambled control ( Fig  2B). These observations also apply to suppression. The typical durations of large-scale suppressions (the blue highlighted sections above n sites = 10) were substantially longer for the actual data ( Fig  2C) than for the phase-scrambled control (Fig  2D), and the typical durations of small-scale suppressions (the blue highlighted portions below n sites = 4) were also longer for the actual data ( Fig  2C) than for the phase-scrambled control (Fig  2D), albeit less apparent.
Average durations of small-scale (n sites ≤ 4, involving 1-4 sites), large-scale (n sites ≥ 10, involving 10+ sites), and intermediate-scale (5 ≤ n sites ≤ 9, involving 5-9 sites) activations and suppressions as well as the probability distributions of n sites for the rest-with-eyes-closed condition are summarized for the four representative frequency bands (q, a, b, and g) in Fig  2E-2L. For all frequency bands, the probabilities of n sites ≤ 2 and n sites ≥ 10 were elevated for both activations ( Fig  2E) and suppressions ( Fig  2I)  ;05 =>?@= !5 =>?@= ! 5 =>?@= 1 − ;05 =>?@= , where N = 60 is the total number of sites, p = 0.08 is the threshold percentile, and n sites is the number of concurrently activated or suppressed sites by chance (the data for the phase-scrambled controls conformed to the Binomial predictions;; not shown). These results suggest that focal (n sites ≤ 2) and large-scale (n sites ≥ 10) activations and suppressions are actively maintained.
Consistent with our observation above (Fig  2A-2D), the average durations of small-scale (n sites ≤ 4) activations (Fig  2F), small-scale suppressions (Fig  2J), large-scale (n sites ≥ 10) activations (Fig  2H), and large-scale suppressions ( Fig  2L) were all extended relative to their phase-scrambled controls (actually, three phase-scrambled controls were averaged for greater reliability) for all frequency bands and for all participants (faint lines). In contrast, the average durations of intermediate-scale (5 ≤ n sites ≤ 9) activations ( Fig  2G) and suppressions ( Fig  2K) were equivalent to their phase-scrambled controls. We note that the average-duration results should be interpreted with the caveat that higher- (or lower-) probability events tend to yield longer (or shorter) average durations even for stochastic variations. Nevertheless, the averageduration results still provide unique information in that a higher temporal probability of activations/suppressions does not necessarily imply longer average durations because a higher temporal probability may result from an increased frequency of unextended activation/suppression periods. We also note that the average durations were generally shorter for higher-frequency bands for both the actual data and their phase-scrambled controls. This reflects the fact that the temporal resolutions of Morlet wavelets were set to be higher for the wavelets with higher center frequencies to achieve a reasonable time-frequency trade-off (see   Fig  6C  and  6E, and Fig  7A,  7C,  and  7E), though suppressions did not show this shift (Fig  6D  and  6F, and Fig   7B,  7D,  and  7F).

Complementary spatial distributions of small-scale and large-scale spectral-power activations and suppressions
The red-blue regions in the spatial-probability-distribution plots are roughly reversed between small-scale (involving 1-4 sites) and large-scale (involving 10+ sites) activations/suppressions (Figs  3-7,  parts  A-F . Note that, because the spatial probability distributions (computed relative to 1/60) have zero means, 5 is equivalent to Pearson's correlation except for the acos transform. For example, 5 = 0° indicates that the distribution of n-site activations/suppressions is identical to the distribution of focal activation/suppression (up to a scalar multiplication factor), with 0°< 5 < 90° indicating that they are increasingly spatially dissimilar, 5 = 90° indicating that they are orthogonal (unrelated), 5 > 90° indicating that they are increasingly spatially complementary, and 5 = 180° indicating a complete pattern reversal (red-blue reversal).
We note that even if the dynamics of activations and suppressions were stochastic, some focal activations/suppressions would occur by chance, which could be weakly clustered in arbitrary regions;; then, multi-site activations/suppressions would be statistically less likely to be detected in those regions due to our use of percentile-based thresholds to define activations and suppressions. This statistical bias may raise 5 for multi-site activations/suppressions to be slightly above 90° even when the underlying dynamics of activations and suppressions were stochastic. To discount this bias, we subtracted the 5 values computed for the phase-

Spatial distributions of large-scale spectral-power activations and suppressions
Where did large-scale (involving 10+ sites) activations and suppressions cluster by frequency band?
For the q band, large-scale activations and suppressions clustered in the posterior regions in the rest-with-eyes-closed condition (Fig  3A-3B, right columns labeled "Large-scale"), whereas they clustered in the frontal and/or lateral-anterior regions in the rest-with-eyes-open-in-dark condition (Fig  3C-3D). In the silent-nature-video condition, intermediate- to large-scale activations clustered in the posterior to lateral-anterior regions (Fig  3E), whereas large-scale suppressions clustered in the posterior regions (Fig  3F).
For the a band, large-scale activations and suppressions clustered in the posterior and medial-anterior regions in the rest-with-eyes-closed condition (Fig  4A-4B). These patterns overall replicated in the two eyes-open conditions except that the medial-anterior cluster was weak in the rest-with-eyes-open-in-dark condition (Fig  4C-4D) and both the posterior and medial-anterior clusters were weaker and the posterior cluster for activations was centrally shifted in the silent-nature-video condition (Fig  4E-4F).
For the b 1 band, large-scale activations clustered in the posterior-to-lateral-posterior and lateral-anterior regions (Fig  5A), whereas large-scale suppressions clustered in the posterior regions ( Fig  5B) in the rest-with-eyes-closed condition. Large-scale activations also clustered in the posterior and lateral-anterior regions in the rest-with-eyes-open-in-dark condition (Fig  5C), whereas large-scale suppressions primarily clustered in the lateral-anterior regions (Fig  5D). In the silent-nature-video condition, large-scale activations clustered in the posterior and lateralposterior regions (Fig  5E), whereas large-scale suppressions clustered in the lateral-anterior regions (Fig  5F).
For the b 2 band, large-scale activations and suppressions clustered in the lateral-posterior and lateral-anterior regions (Fig  6A-6B) in the rest-with-eyes-closed condition. In the two eyesopen conditions large-scale activations and suppressions both clustered in the lateral-anterior regions (Fig  6C-6F).
For the g band, the spatial distributions of large-scale activations and suppressions in all conditions (Fig  7A-7F) were essentially the same as those for the b 2 band in the two eyes-open conditions (Fig  6C-6F), clustering in the lateral-anterior regions ( Figure  7A-7F).

Fig 3. Spatial-probability distributions of spectral-power activations and suppressions as a function of the number of concurrently activated/suppressed sites, nsites, for the q band (4-7 Hz). Activation and suppression are defined as spectral power in the top and bottom 8%
(see main text and Fig  1). The designations of small-scale (involving 1-4 sites) and large-scale (involving 10+ sites) clusters are based on their topographic complementarity (shown here) and their extended average durations (Fig  2). The major row divisions correspond to the three behavioral conditions. For each condition, the spatial-probability-distribution plots are presented in four rows (row 1-row 4). Rows 1 and 2 show the spatial-probability distributions of activations and suppressions, respectively, for increasing numbers of concurrently activated sites, nsites. The above- and below-chance occurrences of activations/suppressions are color-coded with warmer and cooler colors, with the green color indicating the chance level. The values indicate the proportions of deviations from the chance level (1/60);; for example, +0.3 indicates 30% more frequent occurrences than expected by chance, whereas -0.6 indicates 60% less frequent occurrences than expected by chance. Rows 3 and 4 are identical to rows 1 and 2 except that they present the inter-participant consistency of deviations from the chance level as t-values with the critical values for Bonferroni-corrected statistical significance (a = 0.05, 2-tailed) shown on the color bars. We focused on these t-value plots (highlighted and labeled A-F) for making inferences (see main text). In most cases, all participants yielded concurrent activations and suppressions involving up to 18 sites, but in some cases some participants yielded concurrent activations or suppressions involving fewer sites. In those cases, the spatial-probability-distribution plots are presented up to the maximum number of concurrently activated or suppressed sites to which all participants contributed. One can see that small-scale activations and suppressions (columns 1-4) occurred in specific regions while large-scale activations and suppressions (columns 10+) generally occurred in the complementary regions (A-F). This spatial complementarity between smalland large-scale activations and suppressions is quantified in the accompanying line graphs on the right, plotting A, the vector angles (in degrees) between the spatial distribution of focal activations/suppressions and the spatial distributions of multi-site activations/suppressions involving increasing numbers of sites (see main text). A < 90° indicates that multi-site activation/suppression distributions were spatially similar to focal activation/suppression distributions (with A = 0° indicating that they were identical up to a scalar factor), A = 90° indicates that multi-site distributions were orthogonal (unrelated) to focal distributions, and A > 90° indicate that multi-site distributions were increasingly spatially complementary to focal distributions (with A = 180° indicating a complete red-blue reversal). The thick lines with filled circles indicate the mean angles and the gray lines show the data from individual participants. Bonferroni-corrected statistical significance (a = 0.05, 2-tailied) for the negative and positive deviations from A = 90° are indicated with the horizontal lines just below and above the dashed line indicating 90°. The lines with open circles show the vector angles computed from the participant-averaged spatial-probability distributions.

Contextual effects on the spatial distributions of spectralpower activations and suppressions
How did the spatial clustering of spectral-power activations and suppressions depend on context? The spatial scale of activations and suppressions (as indexed by the number of concurrently activated/suppressed sites, n sites ) remained small or large sometimes, but rapidly expanded from small to large or contracted from large to small at other times (e.g. ,  Fig  2A-2D).
Are the distributions of activations and suppressions influenced by these temporal contexts? We

Temporal correlations of the number of activated/suppressed sites between frequency bands
We have seen that the spatial scale of spectral-power activations and suppressions dynamically fluctuate between the characteristic small-scale and large-scale patterns that are frequency specific (Fig  2A-D;;  Figs  3-7). Are the engagements of small- and large-scale networks independent or coordinated across frequency bands? To address this question, we computed the temporal correlation of n site (the number of concurrently activated or suppressed sites) between each pair of frequency bands, using Spearman's r, r sp (which is outlier resistant).
To reduce any effects of spectral leakage (due to the wavelets' spectral-tuning widths;; see Materials and methods), we computed the baseline-corrected r sp by subtracting from r sp the baseline r sp computed with phase-scrambled data (we actually computed three baseline r sp values based on three independent versions of phase-scrambled data, then averaged them). Thus, we obtained some evidence for coordinated engagements of the small-scale and large-scale synchronization networks between frequency bands (as temporal correlations of n sites between frequency bands). The coordination was generally modest (average r sp values being less than 0.5) and weaker between more distant frequency bands, being absent or nearly absent for the q-b 2 , q-g, and a-g pairs. Notably, the pattern of coordination depended on the eyes being closed or open;; when the eyes were closed the a, b 1 , and b 2 bands tended to be somewhat jointly coordinated, but when the eyes were open the a-b 1 coordination tended to dissociate from the emerging b 2 -g coordination (with diminished correlations for the a-b 2 and b 1 -b 2 pairs).

Caveats
While the current analyses used a time-frequency decomposition approach that extracted sinusoidal components from EEG, oscillatory neural activities are not necessarily sinusoidal. As non-sinusoidal oscillations generate harmonics [e.g., [48][49], some of our frequency-specific results may be contaminated by such artifactual harmonics. Nevertheless, it has been shown that macroscopic oscillatory activities averaged across large neural populations such as those reflected in EEG tend to approximate sinusoidal waveforms due to extensive spatial averaging [50]).
EEG spectral power reflects oscillatory as well as non-oscillatory neural activities, with the latter primarily reflected in the 1/f b spectral background that may include contributions from random-walk type neuronal noise generated by the Ornstein-Uhlenbeck process [e.g., [51][52], interplays between excitatory and inhibitory dynamics [e.g., 53], and other processes (see [54][55] for a review). While our use of the temporal derivative of EEG substantially reduced the 1/f b spectral background on the timescale of several seconds for the current EEG data (see Materials and methods), as b is known to fluctuate over time [e.g., 54], it is unclear the degree to which taking the temporal derivative continuously reduced the 1/f b spectral background to highlight oscillatory activity. Thus, our results may reflect spatiotemporal fluctuations in the 1/f b spectral background as well as spatiotemporal fluctuations in oscillatory synchronization and desynchronization.
Might the current results reflect non-neural artifacts? In particular, activities of the ocular and scalp muscles might have generated large spectral power at specific scalp sites. While muscle artifacts tend to occur in the g band [56][57], we observed characteristic small-scale and largescale spatial distributions of spectral-power activations in all representative frequency bands (Figs  3-7). Further, the fact that the average durations of small- and large-scale activations were extended (relative to the phase-scrambled controls) by similar factors for all frequency bands (Fig  2) is inconsistent with the possibility that g band activations may have uniquely reflected muscle artifacts. The strongest evidence we have against any substantive contributions of muscle artifacts to our results is that the characteristic spatial distributions of activations and suppressions generally overlapped, especially for small-scale activations and suppressions and especially for g band (Figs  3-7). Muscle artifacts would not generate consistent spatial distributions of spectral-power suppressions.

General discussion
Oscillatory neural dynamics are prevalent in the brain [58][59][60], contributing to perceptual [17][18][61][62], attentional [14,[21][22][23], memory [15], and cognitive [12][13]16,19] processes (and probably to many other processes), likely through controlling information flow by adjusting phase relations within and across frequency bands [3, 10-11, 22, 60]. While phase relations may be intricately coordinated across neural populations depending on functional demands, an impact of phase realignments would be particularly high (or low) when the oscillatory activities within the interacting neural populations are strongly synchronized (or desynchronized). We thus sought to uncover rules (if any) that govern the spatiotemporal dynamics of maximal and minimal spectral power, which may partly reflect the spatiotemporal dynamics of strong synchronization and desynchronization of cortical neural populations (see Introduction).
To this end, it was important to define maximal and minimal spectral power with appropriate thresholds. Instead of choosing the thresholds arbitrarily (e.g., top and bottom quartiles), we defined them empirically. To characterize how regions of maximal and minimal spectral power spontaneously expanded and contracted, isolated occurrences of maximal and minimal spectral power (occurring exclusively at a single site) may be informative. We thus chose the thresholds for which the occurrences of isolated maximal and minimal spectral power were most prevalent.
Interestingly, the resultant thresholds were universal (virtually identical for different frequency bands across all behavioral conditions) and symmetric for maximal (top 8%) and minimal (bottom 8%) spectral power (Fig  1). This indicates that extreme spectral power at the top and bottom 8% are generally the most spatially isolated in the spatiotemporal dynamics of EEG spectral power. We thus operationally defined the top 8% spectral power as the state of "activation" of neural synchronization and the bottom 8% spectral power as the state of "suppression" of neural synchronization (while acknowledging the various concerns associated with relating EEG spectral power with neural synchronization;; see Introduction and Caveats).
Using these definitions, we obtained converging evidence suggesting that spectral-power activations and suppressions are organized into spatially segregated networks, relatively Taken together, these results suggest that the spatiotemporal dynamics of maximal and minimal spectral power, potentially indicative of the spatiotemporal dynamics of strong synchronizations and desynchronizations of oscillatory neural activities, are partly characterized by spatially segregated small-scale networks where regional populations are strongly synchronized or desynchronized in relative isolation and large-scale networks where many regional populations are strongly synchronized or desynchronized concurrently in a highly cooperative manner. These small-scale and large-scale networks of concurrently synchronized/desynchronized neural populations may confer an overarching dynamic structure that may constrain the impact of task-specific realignments of phase relations within and across frequency bands and brain regions. Future research may investigate how phase-relation realignments are coordinated with the status (strongly synchronized or desynchronized) of these small- and large-scale synchronization networks to optimize information processing.
Our results also suggest that these small-scale and large-scale networks are frequency specific (Figs  3-7  and  Figs  8-12). Speculating on the potential relationships between the frequency-specific networks identified here and the extensive literature on task-dependent oscillatory activities involving different frequency bands is beyond the scope of the current discussion. Instead, we summarize some notable aspects of the frequency specificity of the small- and large-scale synchronization/desynchronization networks. First, in the eyes-closed condition, the small-scale networks for the q, a, b 1 , and b 2 bands all included the frontal region, while the large-scale networks systematically shifted from including primarily posterior regions for the q band, posterior and medial-anterior regions for the a band, posterior and lateralanterior regions for the b 1 band, primarily lateral-anterior regions for the b 2 band, and consistently lateral-anterior regions for the g band (Figs  3-7,  parts  A  and  B). Second, regardless of behavioral condition, the small-scale networks were consistently localized in the medialcentral-posterior regions and the large-scale networks were localized in the lateral-anterior regions for the g band (Fig  7). Third, the small- and large-scale networks for the b 2 band the engagements of small- and large-scale synchronization networks were only modestly coordinated (r sp < 0.5) across frequency bands, and virtually uncoordinated between distant frequency bands (Fig  13).
To conclude, many studies have examined the spatiotemporal relations of spectral amplitude and phase within and across frequency bands by analyzing correlation-matrix structures to identify (static, time-averaged) spatial networks and their connectivity that may be associated with specific behavioral functions and mental states. What was unique about the current study was to investigate general rules governing the spatiotemporal dynamics of networks of strongly synchronized and desynchronized neural populations by tracking the dynamics of spontaneously emerging and dissipating clusters of maximal and minimal spectral power. In this way, we were able to obtain converging evidence suggesting that prolonged periods (compared with stochastic dynamics) of strong synchronization and desynchronization occur in small-scale and large-scale networks that are spatially segregated and frequency specific, partly segregating the relatively independent and highly cooperative oscillatory processes.