{'fraction_non_alphanumeric': 0.02823977164605138, 'fraction_numerical': 0.010104662226450999, 'mean_word_length': 5.400852618757613, 'pattern_counts': {'":': 0, '<': 6, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Inter-subject phase synchronization and the dynamics of human cognition

Massive whole-brain blood-oxygen-level dependent (BOLD) signal modulation (up to 95% of brain voxels) in response to task stimuli has recently been reported in functional MRI investigations. These findings have two implications. First, they highlight inability of a conventional ‘top-down’ general linear model approach to capture all forms of task-driven brain activity. Second, as opposed to a static ‘active’ or ‘non-active’ localization theory of the neural implementation of cognitive processes, functional neuroimaging should develop and pursue dynamical theories of cognition involving the dynamic interactions of all brain networks, in line with psychological constructionist theories of cognition. In this study, we describe a novel exploratory, bottom-up approach that directly estimates task-driven brain activity regardless of whether it follows an a priori reference function. Leveraging the property that task-driven brain activity is associated with reductions in BOLD signal variability, we combine the tools of instantaneous phase synchronization and independent component analysis to characterize whole-brain task-driven activity in terms of group-wise similarity in temporal signal dynamics of brain networks. We applied this novel framework to task fMRI data from a motor, theory of mind and working memory task provided through the Human Connectome Project. We discovered a large number of brain networks that dynamically synchronized to various features of the task scan, some overlapping with areas identified as ‘active’ in the top-down GLM approach. Using the results provided through this novel approach, we provide a more comprehensive description of cognitive processes whereby task-related brain activity is not restricted to dichotomous ‘active’ or ‘non-active’ inferences, but is characterized by the temporal dynamics of brain networks across time. Significance Statement This study describes the results of a novel exploratory methodological approach that allows for direct estimation of task-driven brain activity in terms of group-wise similarity in temporal signal dynamics, as opposed to the conventional approach of identifying task-driven brain activity with a hypothesized temporal pattern. This approach applied to three different task paradigms yielded novel insights into the brain activity associated with these tasks in terms of time-varying, low-frequency dynamics of replicable synchronization networks. We suggest that this exploratory methodological approach provides a framework in which the complexity and dynamics of the neural mechanisms underlying cognitive processes can be captured more comprehensively.


Introduction
Task-based fMRI has produced a wealth of large-scale function-structure mappings representing associations between mental processes and unique regions or networks of the brain [1][2][3][4][5] . However, a consensus localization of mental functions to unique cortical/sub-cortical areas has yet to emerge. Recent findings reminiscent of early theories of cortical mass action 6,7 have demonstrated that time-locked activation is observed in a majority of the brain (in some cases, over 95% of the brain) in response to external task presentations [8][9][10][11][12] . For example, using massive within-subject averaging, Gonzalez-Castillo et al. 8 observed that the majority of the brain exhibits time-locked activation to a simple visual stimulation and attention task, with substantial variation of hemodynamic responses across different regions of the brain.
These results suggest that it is not a question of 'if' most brain regions are involved in any given task, but rather 'when.' These results further motivate a dynamical theory of cognition that goes beyond dichotomous decisions of 'active' or 'non-active' brain areas. Rather, an adequate description of psychological processes involves identifying the temporal dynamics of brain networks periodically synchronized to external task-relevant events of the task presentation. A constructionist account of cognitive processes 13,14 provides a theoretical grounding for such a theory whereby cognition emerges from the interaction and temporal dynamics of more basic domain-general, functional brain networks (e.g. fronto-parietal network, default-mode network, etc.). Therefore, an adequate description of the cognitive processes involved in an experimental task requires examination of all brain networks that periodically synchronize (simultaneously or consecutively) to various task features.
In typical fMRI cognitive neuroscience paradigms, a brain region is understood to be involved in a task if that region exhibits blood-oxygen-level dependent (BOLD) variation that follows a hypothesized temporal structure. This 'top-down' approach often involves the application of a general linear model (GLM), and a reference function corresponding to task events that is convolved with a hemodynamic response function (HRF) [15][16][17] . However, any brain regions or networks involved in a given cognitive process not predicted by conventional reference functions would not be detected by this approach. Most importantly, the 'top-down' approach would not capture complex temporal dynamics that a given task may produce in activation patterns across the brain.
We propose a 'bottom-up' exploratory approach for the analysis of task fMRI data that directly estimates task-driven brain activity in a data-driven manner, without the application of a hypothesized temporal structure. The estimation of task-driven brain activity is non-trivial, as brain activity is highly dynamic and structured even in the absence of stimulus presentations, owing to spontaneous activity [18][19][20][21] and signal fluctuations due to noise sources 22,23 . However, a potential marker of task-driven brain activity (opposed to spontaneous activity or noise) is variability reduction in the neural signal post-stimulus. A reliable property of task-driven BOLD activity 24,25 , and firing rates and membrane potentials from single-cell recordings 26,27 , is poststimulus signal variability reduction. An approach incorporating the neural variability reduction phenomenon could be used as an exploratory measure of task-driven brain activity. Established inter-subject synchronization measures provide the foundation necessary for detecting taskrelated signal variability reductions [28][29][30][31][32] , assuming a brain region is entrained to a stimulus in a common way across participants. The logic of this approach is as follows: in individuals concurrently experiencing the same stimulus, a task-responsive brain region entrained to that stimulus would produce similar or conserved temporal dynamics across subjects 29 as a result of the common entrainment of that voxel to the stimulus condition.
Conventional 'static' inter-subject correlation approaches 30,31 provide an average measure of brain synchrony across the entire task at each voxel. For a dynamical measure of inter-subject synchronization, the current paper utilizes an instantaneous phase synchronization measure 28,32 for voxel-wise assessments of synchronization at each time point (Figure 1), followed by an independent components analysis (ICA) 33,34 applied to the voxel-wise synchronization time series. This novel methodology identifies time-varying, task-driven brain network dynamics without dependence on a priori reference functions, and provides a framework for the examination of task-relevant whole-brain temporal dynamics. Figure 1. Using inter-subject synchronization to study task-driven brain responses. If one assumes that a task-responsive brain region (e.g. dorsal anterior cingulate cortex; dACC) exhibits a common response across participants (e.g. increase in signal amplitude), one can implement an inter-subject synchronization approach that can examine that brain region's across-subject variability at each time point by measuring synchronization of the BOLD signal across participants at that time point. I) Three subject's dACC time series are displayed in separate colors, and all demonstrate a similar increase in signal amplitude in the task-blocks. II) In order to focus our analysis on 'pure' temporal structure across subjects (as opposed to magnitude differences across subjects), a phase representation of each subject's time series is constructed 28 .

III)
From the phase representation of each signal, we can identify group-wise synchronization estimates for each time point by essentially calculating the (inverse) average angular distance between each subject's phase signal. Using group-wise synchronization estimates at each time point, we can examine synchronization dynamics across the task scan in a data-driven manner, without any reference to a hypothesized on-and off-task block structure or HRF specification. Phase calculations demonstrate higher phase synchrony during a task block (time point = 55) compared to non-task blocks (time point = 5 and time point = 30).
There are three methodological and theoretical advantages of this methodology over the traditional GLM approach: 1) a reference function of task events or hemodynamic response function (HRF) is not required to detect task-responsive brain regions, 2) the synchronization approach does not assume that task-driven brain responses follow a single, simple form (e.g. transient, sustained or mixed activation) of voxel-wise activity, and 3) the approach allows for assessing dynamical or time-varying task-related brain networks. To demonstrate the viability and benefits of this novel methodology when studying task-driven brain responses, we applied this approach to three large-sample task Human Connectome Project (HCP) 35 fMRI data sets: motor, theory of mind, and working-memory.
The results demonstrate that this alternative methodological approach recapitulates traditional GLM activation maps, but more importantly, it also identifies novel time-varying replicable synchronization networks. The identification of these new novel synchronization networks, in addition to brain areas commonly identified by a traditional GLM approach, provides a richer, fuller description of cognition whereby task-related brain activity is not restricted to dichotomous 'active' or 'non-active' inferences, but rather is more comprehensively described by the temporal dynamics of brain networks across time.

Instantaneous Phase Analysis
As phase analysis is most effective on a band-limited signal 28 , a data-driven estimation of the frequency band for all three tasks was conducted to guide the selection of a frequency band of interest. A static inter-subject synchrony analysis (see Experimental Procedures) revealed that a low frequency sub-band (~0.01 -0.085 Hz) demonstrated the highest level of average BOLD synchrony across subjects. This sub-band was used for further analyses ( Figure   S1). The average BOLD synchrony maps of this sub-band for each task overlapped significantly with the z-scored 'activation' maps derived from the GLM reference-function approach (r Motor = 0.76, r TOM = 0.85; r WM = 0.83; S1 Figure).
Next, instantaneous phase synchronization analysis 28 was conducted on this lowfrequency sub-band, providing group-wise synchronization time-course estimates at each voxel.

Synchronization Dynamics During the Motor Task
The motor task was chosen because the neural correlates of movement are well understood 36 , providing a validation test for the synchronization approach. The activation maps for each motor movement produced by the standard GLM-reference function approach corresponded precisely to their expected task-relevant brain areas (Figure 2). For example, left motor cortex activation was associated with right-hand motor movements while fronto-parietal and visual activation was associated with visual cue trials.

Figure 2. Activation Maps from traditional GLM-Reference Function
Approach. Z-scored unthresholded activation maps derived from the standard reference functions provided for the motor, theory of mind, and working-memory task. The activation maps model either the increase in BOLD activation from baseline due to a task condition, or the relative activation/de-activation between two task-conditions (i.e. subtraction contrasts).
Three of the ten components derived from the ICA synchronization analysis were classified as noise (S3 Figure) as they had many voxels with strong weights in either white matter, cerebrospinal fluid (CSF) or along the surface of the brain corresponding to movement artifacts. All seven non-noise components showed a characteristic pattern of peaks and troughs (i.e., local maxima and minima) of synchronization across the course of the scan with varying degrees of periodicity (Figure 3). Significant synchronization peaks were defined as those collection of synchronization time points with estimates greater than a significance threshold The results for the visual cue with the standard GLM-reference function approach revealed strong activation in voxels that encompassed both visual and fronto-parietal control areas ( Figure 2). However, the novel synchronization approach revealed differing temporal dynamics between visual and fronto-parietal control areas elucidating the temporal interplay between these two brain areas. Significant peaks in the synchronization time course of C6

Synchronization Dynamics During the Theory of Mind Task
The theory of mind task consisted of short video clips of either interacting or randomly moving shapes, and is used to study higher-level processing of dynamic visual stimuli. The activation maps produced by the standard GLM reference-function approach were strongly similar between the theory of mind and random blocks (Figure 2). Activation for both block types was observed in primary and higher-order visual cortices, and fronto-parietal areas.
Activation differences between the theory of mind and random blocks were primarily observed in lateral occipital cortices, lateral temporal-parietal junction, and inferior frontal gyri.
Two of the 10 components derived from the ICA phase synchronization analysis were classified as noise while one component did not replicate in the confirmatory sample and was not interpreted further (S3 Figure). Four of the seven non-noise components were observed to have strong spatial weights predominantly in the primary and higher-order visual cortices (C2, C4, C5, and C7; Figure 4), perhaps related to the fact that each task block required careful visual attention to moving task stimuli. The other components (C1, C3 and C6) were observed to have strong spatial weights predominantly in areas of the fronto-parietal control network (C1 and C6) and temporal lobes (C3). The synchronization dynamics of the seven signal components can be roughly divided into off-task-block (C2, C5 and C7), on-task-block (C1 and C6), task-block specific (C3) and non-block (C4) components.
C3 was classified as a task-block specific component because its synchronization time series positively correlated with theory of mind block types (r = 0.71, p < 0.0001). Additionally, the C3 spatial weights within the bilateral fusiform gyri and right tempo-parietal junction (TPJ) correspond to brain areas consistently implicated in the theory of mind literature 38,39 .
Interestingly, the spatial weights of C3 significantly overlapped (r = 0.41, p < 0.0001) with the theory of mind-minus-random contrast (Figure 2 off-task block components showed a characteristic pattern of synchronization dynamics across the duration of the theory of mind task (Figure 4). Specifically, the on-task block components were observed to have significant synchronization peaks during the last seconds of the 20s taskblocks extending into the off-block periods, with subsequent synchronization peaks of the offtask block components, in the off-block periods. The onset of cognitive processing associated with C1, and subsequent motor processing associated with C6 (mean TR difference between synchronization peaks of C1 and C6: 2.01 TRs, SD: 0.88) towards the latter end of the task-block is consistent with the fact that after the 20s on-block video watching period, the participants were asked to rate the video in terms of intentional or randomly acting shapes. During the rating period and subsequent fixation period, participants were presented with static visual stimuli, consistent with the onset of synchronization peaks of the different visual components C2, C5, and C7. corresponding thresholded spatial weights of C1 through C7, and the GLM reference functions (random shape movement in red, and intentional shape movement in yellow) for the task. Thresholds for each synchronization time course are represented by the red dotted-lines (with the corresponding value to the left of the plot). B) Visual comparison of the on-and off-task block component synchronization time courses (both block types are combined in one reference function and are presented in yellow). On-block task component (C1 and C6) synchronization time courses are presented in blue and observed to have significant synchronization peaks during the last seconds of the 20s task-blocks extending into the off-block periods. Off-block task component (C2, C5 and C7) synchronization time courses are presented in red, and are observed to have significant synchronization peaks shortly after the on-black task component peaks during the off-block periods. For visual reference, statistically significant peaks in the synchronization time courses for C1 (on-block component) and C2 (off-block component) are marked by vertical blue-and red-dotted lines. Significance thresholds for the synchronization time courses are represented by the black dotted-lines (the threshold for C6 was 0.56, but presented as 0.57 for visualization purposes).

Synchronization Dynamics During the Working-Memory Task
The working-memory task was a visual N-back task with 0-back and 2-back conditions consisting of category-specific visual stimuli. The activation maps for the 0-back and 2-back conditions produced by the standard GLM-reference function approach were similar, with the strongest activation values in areas of the fronto-parietal control network (Figure 2). Differences in activation associated with each category-specific stimulus (body, face, place, and tool stimuli) were observed in the primary visual and inferior-temporal cortices.
One of the ten components derived from the ICA phase synchronization analysis was classified as noise (S3 Figure). Four non-noise components ( Figure 5) were grouped together because they had strong spatial weights in visual cortices and similar synchronization time courses. The spatial weights of C1 through C4 demonstrated that each component represented a unique partition of primary and secondary visual cortices. The spatial weights for the four components overlapped to a moderate degree with the differential activation areas associated with each category-specific stimuli: C2 was spatially correlated with body stimuli activation (r = 0.49, p < 0.0001), C1 and C4 were spatially correlated with place stimuli activation (C1: r = 0.51; C4: r = 0.43; p's < 0.0001), C3 was spatially correlated with tool stimuli activation (r = 0.43; p < 0.0001), and C4 was not strongly correlated with any of the four stimuli.
While the subtraction contrasts between the stimulus blocks revealed differential activation patterns in visual cortices, the phase synchronization approach revealed that visual areas, represented by components C1-C4, demonstrate predominantly similar temporal dynamics to all types of stimulus blocks, with significant synchronization peaks occurring at approximately the same time points, but with differences in the degree of synchronization at each peak time point. In relation to the reference functions provided in the task, the synchronization time courses for all four components contained approximately 16 significant synchronization peaks, corresponding to the 16 task blocks of all types presented to the participants in the workingmemory task. However, increases in synchronization estimates did not coincide with task blocks, Other interesting findings pertain to the other five non-noise components (Figure 5).
Examination of the synchronization time courses of C5, C7, and C8 reveals that these components exhibit significant synchronization peaks early in the working-memory task, but diminished, non-significant synchronization peaks thereafter, indicating habituation of these networks to the working-memory task after repeated task-block presentations, or their involvement in task-set initiation. The spatial patterns of C5, C7 and C8 suggest these components correspond to the posterior parietal and left-dominant prefrontal brain areas, default mode network, and bi-lateral motor cortex/basal ganglia areas, respectively. Of note, in addition to strong spatial weights for C5 in lateral posterior parietal and prefrontal areas, they were also observed in the precuneus, a default-mode network hub 40 , indicating that default-mode network regions may synchronize with executive control regions during certain time points of the working-memory task 41,42 . Strong spatial weights for C7 were also observed in the anterior caudate nucleus, an area that forms a central part of a cortico-striatal loop with frontal regions and known to be important in cognitive processing 43,44 . Spatial weights of C6 and C9 corresponded to task-positive, executive-control brain areas and medial occipital/middle cingulate cortices, respectively. Significant synchronization peaks in the time courses of C6 and C9 corresponded closely in time to peaks of the visual components (C1-C4), suggesting that C6 and C9 are responsive to similar stimuli.

Discussion
The development of a data-driven approach for examination of task-driven brain responses requires a fundamental shift in both conceptual framework and analytic strategy. Here we demonstrate the utility and power of an inter-subject phase synchronization approach to describing task-driven brain responses. The spatial patterns and synchronization time courses of each network replicated across two independent samples of subjects. Importantly, the synchronization networks for each task spanned the majority of the brain's cortical and subcortical regions, indicating that the task-response of the brain is not 'localized' to a single network or region, but in line with earlier predictions 45 , the majority of the brain responds in differing ways to task demands. The inter-subject phase synchronization approach goes beyond a traditional "top-down" GLM analysis and provides a principled way to determine 'when' and 'where' these task-driven responses occur during the course of an experiment. Below we discuss what the findings from the inter-subject synchronization approach applied to a motor, theory of mind and working memory task might imply for a dynamical theory of motor action, theory of mind and visual working memory processes, respectively.

Dynamics of Motor/Action Processes
Applied to a simple motor mapping task, we found that the synchronization approach achieved precise localization of task-driven brain networks, with each network dedicated to the movement of a unique body part. In addition, the approach revealed 'non-motor' networks with temporal dynamics related to other events in the task. While the 'visual cue' reference function with the top-down GLM approach identified both visual and FPN as active during this period of the task, our approach revealed these two networks do not respond simultaneously to the task, but consecutively. The results revealed that the FPN significantly synchronized before the onset of each motor block. In addition, the spatial pattern of this network also included primary motor areas, indicating that these regions may serve as a preparatory process for motor/action control.
This observation is further supported by previous findings of activation in the FPN and motor cortex during action preparation [46][47][48] . Synchronization of the FPN is followed by synchronization of the visual network, including areas of the posterior parietal cortex, that occur close in time to the visual cue, reflecting visuospatial processing of the visual cue indicating the appropriate motor movement. Together, these findings indicate a sequence of motor preparation, visuospatial processing, and motor action encompassing fronto-parietal, visual and motor areas of the brain that constitute a successful motor action. Importantly, this information regarding temporal dynamics of brain responses during task performance cannot be obtained using a traditional GLM approach.

Dynamics of Theory of Mind Processes
The synchronization approach applied to the theory of mind task produced several visual and cognitive networks with complex temporal dynamics not predicted by the 'top-down' GLM approach. Only the bilateral fusiform/right TPJ network (C3) was related uniquely to a particular block of the task. Consistent with these brain areas role as a potential theory of mind 'module' 38,39 , this network significantly synchronized only during the theory of mind block types. These areas were also identified by the subtraction contrast between the theory of mind and random blocks from the top-down GLM approach. However, examination of other network synchronization dynamics challenges the inference that these regions are selectively responsible for theory of mind processing. For example, the posterior parietal network (C4) exhibited sustained synchronization across the entirety of both task runs (theory of mind and random blocks), even during synchronization of the bilateral fusiform/tempo-parietal junction network (C3). This suggests that the posterior parietal network is a sustained attention process that biases the brain toward relevant sensory signals of the task, consistent with previous research 49,50 .
In addition to this network, a network (C1) consisting of the dACC, PCC and left temporal lobe, and a network (C6) consisting of the supplementary and left motor cortex, exhibited significant synchronization towards the latter end of all task blocks. The PCC and left temporal lobe are parts of the DMN 51,52 , which has been implicated in theory of mind processing 53,54 . The dACC is often considered a crucial component of the salience network 55 . Because these regions synchronize after the fusiform/TPJ network and synchronize in both random and theory of mind blocks, they may constitute a form of theory of mind processing important for the subsequent decision of intentional versus random interactive stimuli, as opposed to immediate processing of the stimuli in both blocks. Consistent with the requirement of a motor response to indicate the participant's answer at the end of the task block, synchronization of the supplementary/left motor cortex may represent a preparatory motor signal for the subsequent motor response. Overall, these findings suggest that a single region or network (e.g., TPJ), as identified via a GLM analysis does not adequately capture the rich temporal dynamic involved in the theory of mind task. Rather, an inter-subject phase synchronization approach identifies a number of networks spanning many cortical structures with variable task-driven temporal dynamics across the course of the task.

Dynamics of Visual Working Memory Processes
The synchronization approach applied to the visual N-back task with four categories of visual stimuli produced unique functional partitions of visual and posterior parietal areas. Four visual/parietal networks exhibited significant synchronization towards the end of each workingmemory task block reflecting synchronized de-activations of these regions across subjects (S5 Examination of the other networks discovered through the synchronization approach reveals that primary visual and higher-order visual areas are not the only areas responsible for short-term maintenance of visual features. In fact, a number of networks, including the default mode network, the fronto-parietal network, basal ganglia, the dACC/PCC network observed in the theory of mind task, and a precuneus/DLPFC/TPJ network, exhibited synchronization to Nback task blocks. These findings suggest that a theory of visual working memory processes involving neural processing within a single brain network or brain region is inadequate. Rather, a comprehensive theory of working memory processing involving a coalition of fronto-parietal and visual networks provides a more comprehensive description of visual working memory processes.

Dynamical Theory of Cognition and the Inter-Subject Synchronization Approach
Within a complex adaptive systems framework [64][65][66]

(Bolt, Anderson and Uddin, Under
Review), the experimenter is interested in the temporal dynamics of the neural system as it evolves through time. The complex adaptive system framework compliments a dynamical theory of cognition where task-based psychological processes are described in terms of the temporal dynamics of brain networks as they synchronize simultaneously or sequentially over time.
Conventional 'top-down' GLM approaches reduce this dynamical process into a dichotomous 'active/non-active' inference on a localized set of regions or networks. We argue that the intersubject synchronization approach provides task fMRI researchers with the ability to recover traditional GLM activation patterns while also identifying novel low-frequency synchronization dynamic brain networks across time. Accordingly, the dynamical theory of cognition proposed in this study is a network-based theory of cognition, whereby psychological processes are constructed out of a dynamic coalition of brain networks 13,67 , as opposed to the fixed functions of a few brain regions or a single network. Consistent with arguments that psychological processes map onto a large range of functionally distinct brain networks 14,68 , the synchronization approach discovered a large number of networks involved in each task, covering a large expanse of cortical and sub-cortical brain structures.

Limitations of the Inter-Subject Synchronization Approach
While synchronization provides a flexible exploratory approach for the study of taskdriven brain responses, the approach does require certain assumptions to be met. First, the approach requires that the task run presented to each participant is identical in timing across all participants. This is essential to the approach, as the synchronization metric measures the extent of similar temporal dynamics in the time course across participants at each time point. Thus, task designs that utilize randomized presentation of task stimuli across participants would not be appropriate for the approach presented here, nor would tasks with counterbalanced task blocks across participants, unless the BOLD time courses are reordered before the analysis. Second, differences in hemodynamic responses and cerebral blood flow dynamics between participants would have adverse effects on the synchronization metric across participants, to the extent that these differences result in disparate timing in hemodynamic responses. In the traditional GLM reference function approach, these differences can be partially accounted for by additional regressors that model between-subject differences in hemodynamic durations and onset delays 69 .
However, in the future, techniques accounting for these between-subject differences could be conceivably applied to the synchronization approach as well. As demonstrated by the current results, the approach still yields precise estimates despite these concerns.

Conclusion
The goal of this study was to provide empirical support for a dynamical theory of cognitive processes through use of a methodological framework of synchronization dynamics that incorporates insights regarding task-driven signal variability into an exploratory task fMRI approach. The synchronization approach produced rich and varied insights into the dynamical neural interactions underlying the psychological processes involved in simple motor responses, as well as higher cognitive functions. Future studies are needed to develop the synchronization approach into a standardized methodological approach for analysis of task fMRI. For example, simulation studies could provide insights into the sample size and task designs necessary to achieve robust and replicable synchronization estimates. We believe that the dynamical study of cognitive processes made possible by the inter-subject synchronization approach implemented in the current study provides a valuable tool for cognitive neuroscientists.

fMRI Data
Neuroimaging data from 150 unrelated, healthy, right-handed adults (Age Ranges:  Louis, MO). All participants gave informed consent before participating in the study, as described in Van Essen et al. 70 . Three task scans, a motor task, a theory of mind task, and working-memory task were used for analysis 35 .

Task Descriptions
All details for the motor, theory of mind and working memory task used in this study are provided in 35 . The motor task was chosen because the task involved simple motor movements and the movement-brain activation mappings are well understood 36 , which provides an initial test case for the synchronization approach. In the task, participants are presented with visual cues that ask for movements of five specific body parts: tap left or right fingers, squeeze left or right toes, or move their tongue. The task involved two runs which both consisted of 13 movement blocks lasting 12s, preceded by a visual cue lasting 3s, and three fixation blocks lasting 15s. The reference functions used for the task were provided through the HCP, and included five regressors modeling the five specific movement types, and one regressor modeling the visual cue that indicated the start of each movement block. In addition, an all movement regressor was created that modeled all movement type blocks.
To test the synchronization approach on a task involving higher cognitive processing, the theory of mind and working-memory tasks were chosen. The theory of mind task involved higher-level processing of dynamic visual stimuli, consisting of short video clips of either interacting or randomly moving shapes, and rating periods where the participants indicated either of three choices: the objects had a social interaction, Not Sure, or No Interaction. The entire task included two runs, each including five 20s video blocks: 2 Interaction (theory of mind) and 3 Random for run one, and 3 Interaction and 2 Random for the run two; and five 15s fixation blocks. The reference functions used for this task were provided through the HCP, and included two regressors for interaction (theory of mind) video blocks and random video blocks, respectively (the rating period was not modeled). In addition, an all-block regressor was created that modeled both interaction and random video blocks together. The working-memory task was a N-back task that involved visual processing of category specific visual stimuli. The entire task consisted of two runs, that each included ½ 0-back (a target visual cue is presented at the beginning of each block and the participant is directed to respond when that visual stimulus is presented) and ½ 2-back blocks (the participant is directed to respond when the current visual stimulus is identical to one presented two presentations back) that presented one of four stimulus types blocks (body parts, faces, places and tools). Thus, there were eight 25s task blocks for each run representing all possible combinations of task type (0back and 2-Back) and stimulus type (body parts, faces, places and tools), along with four 15s visual fixation blocks. At the start of each block, there is a 2.5 sec visual cue indicating the task type (0-back versus 2-back), followed by ten 2.5s trials, where a stimulus was presented for 2s, followed by a 500ms inter-trial interval. The reference functions used for this task were provided by the HCP, and included eight regressors each modelling one of the eight possible task blocks (e.g. 0-back face block). In addition, four regressors were created modelling the four visual stimulus types (regardless of task type), and an all-block regressor modeling all task blocks.

Data Preprocessing
Minimally preprocessed data provided through the HCP were used for further analyses.
The minimal preprocessing pipeline involved gradient distortion correction, motion correction, registration to the Montreal Neurological Institute (MNI) template, and intensity normalization.
The details of the minimal preprocessing pipeline are described in 71 . Additional preprocessing steps included demeaning, variance normalization (normalizing the data to their standard deviations from the mean, z-score) and concatenation of the time series from the right-left and left-right runs, respectively for each task using the Connectome Workbench 72 . Data was resampled to 3mm voxel size for computational feasibility, time courses were despiked using AFNI's 3dDespike, an interpolative scrubbing procedure, and time-series were then detrended using FSL's nonlinear Gaussian weighted least-squares fitting with a cutoff of 100s 17 . Of note, this high-pass filtering procedure only removes a part of the low-frequency signal below the cutoff of 100s and frequency bands can be still be studied below this cutoff, as demonstrated by other inter-subject correlation applications 73 . The functional data were then spatially smoothed (5mm full width at half maximum) with FSL, and nuisance covariate regression was performed (Friston's 24 motion parameters, namely each of the 6 motion parameters of the current and preceding volume, plus each of these values squared, ventricle and white matter signals) using the Data Processing and Analysis for Brain Imaging (DPABI) toolbox 74 . No participants included in the analysis displayed gross motion (relative Root-Mean Squared-Framewise Displacement 75 ; RMS-FD < 0.55mm; 76 .

Standard General Linear Model Activation Estimates
Large-sample (n = 486) activation maps derived from the standard general linear model for each reference function were collected from NeuroVault 77 , to ensure that differences with the synchronization approach were not the result of insufficient statistical power. A conventional mixed-effects GLM analysis was conducted to derive activation estimates for each reference function, and is described in 35 .

Determination of Frequency Band for Phase Analysis
Because the instantaneous phase synchronization approach is most effective for a bandpass limited signal 28 , we first conducted an eigenvalue synchrony analysis 29 for all three tasks across frequency sub-bands to determine the frequency band that demonstrated the strongest average inter-subject synchrony. The eigenvalue synchrony analysis is a static inter-subject synchrony analysis, because it computes inter-subject synchrony across the course of the entire task scan. This approach allowed for a data-driven assessment of average synchrony in each frequency band to determine which band to use for the instantaneous phase synchronization analysis. Four frequency sub-bands were constructed through the stationary wavelet transform (SWT) as described by Kauppi et al. 73 and implemented in the Inter-Subject Correlation (ISC) toolbox 32 . The SWT is more desirable over standard implementations of discrete wavelet transforms, as it is time-invariant, making the filter bank construction robust to small differences in hemodynamic lag between participants that could lead to large inconsistencies in the estimation of inter-subject synchronization. The SWT algorithm operates through successive splitting of low pass-filtered signals into new low-and high-pass signals 73 , and results in a logarithmic scale of the frequency sub-bands. We conducted a 4-scale SWT decomposition, resulting in 4 frequency sub-bands ranging from higher (Band 4) to lower frequency bands (Band 1). The approximate frequency characteristics, calculated as the frequency range in which 90% of spectral power is contained, of each band is: Band 1: 0.01 -0.085 Hz, Band 2: 0.08 -0. 18  The inter-subject eigenvalue synchrony approach was applied within each sub-band. The approach is conducted on a voxel-by-voxel basis and provides an assessment of group-wise synchrony in the time series across all subjects at each voxel. The strength of synchronization for each sub-band was computed by simply averaging the group-wise synchronization estimates across all voxels within the brain. The resulting eigenvalue maps (representing eigenvalues at each voxel in the brain) were thresholded using the permutation testing framework implemented by Kauppi et al. 32 , but adapted for constructing a null distribution of eigenvalues. For further details regarding the inter-subject eigenvalue synchrony analysis and permutation testing framework implemented in this study see Supplemental Experimental Procedures.
In addition to determination of the strongest synchronization sub-band, the group-wise static synchronization estimates at each voxel across frequency sub-bands were compared with the 'activation' estimates (z-score estimates) derived from the standard GLM approach using the conventional reference function. In particular, static synchronization estimates for the motor, theory of mind and working memory task were spatially correlated with the absolute-valued all motor movement, theory of mind, and 2-back activation maps, respectively. This allowed for an assessment of the degree of correspondence between the identification of task-driven brain responses between the static inter-subject synchrony analysis and the standard GLM approach.

Instantaneous Phase Synchronization Calculation
The strongest synchronized frequency band, in terms of greatest average synchrony (i.e. eigenvalues) across the brain, was used for the instantaneous phase synchronization approach.
Phase-based representations of fMRI signals have been used successfully in other fMRI analyses 25,78 , and has been previously validated for measurements of inter-subject synchronization by

Independent Component Analysis of Synchronization Time Series
The result of the instantaneous phase synchronization analysis is a time-series of synchronization values for each voxel in the brain, representing the average synchrony (the average absolute angular distance) across participants for each time point (TR). Rather than a conventional ROI-based analysis of synchronization, we chose to use a data-driven independent component analysis (ICA) that incorporates synchronization time signals across the entire brain to estimate possible synchronization networks that 'pipe in' and 'fade out' of the observed synchronization signals across the course of the task scan. The ICA was implemented through FSL's MELODIC software 33 . This approach is equivalent to a single-subject ICA applied to group-level synchronization time series across all voxels in the brain, rather than the original signal time-courses of all voxels.

Assessment of Number of Components and Replication
We estimated a range of lower model-order ICAs, including 10, 15 and 20 component solutions. Lower model-order ICAs were estimated for two reasons: 1) As most traditional task-fMRI analyses are concerned with a small subset of brain regions involved in any one task, a lower number of synchronization networks were estimated, and 2) the components are estimated from a 'single subject' or single brain of group-wise synchrony time series, which contains less data points (as opposed to group-level ICAs) for robust/replicable estimation of higher-order model ICAs. Of the 10, 15, and 20 component ICA solutions, we chose the solution that was most replicable in another confirmatory sample of 75 participants. 'Replicability' was measured in three ways: 1) the number of components that had 'matching' component pairs in the confirmatory sample in terms of visual examination between the original and confirmatory ICA solutions, 2) the spatial correlation between the 'matching' unthresholded component pairs from the original and confirmatory ICA solutions, and 3) the temporal correlation between the synchronization time series (computation described below) of the 'matched' components from the original and confirmatory ICA solutions. In addition to the determination of the number of components, the confirmatory sample also allowed an assessment of the degree to which the synchronization approach replicates across samples.
After ICA estimation of the chosen model-order, classification of components into noise and non-noise components was conducted in the same manner as ICA applied to normal BOLD time series: components with many strongly weighted voxels in white matter or cerebrospinal fluid (CSF) were classified as noise

Component Synchronization Time Series and Statistical Significance
We implemented a bootstrap resampling procedure described in Glerean et al. 28

GLM Reference Functions and Synchronization Comparison
As described above, we used the convolved block regressors of the GLM from the motor,

Comparison of Average BOLD Dynamics with Synchronization Estimates
Another question of interest is the relationship at any time point between average BOLD magnitude across participants, and the degree of synchronization observed across participants.

Comparison of Functional Connectivity Relationships in Synchronization and BOLD Time Series
An important question is the extent that functional connectivity relationships in the group-wise synchronization time series, modeled as spatially independent components of synchronization dynamics, reflect functional connectivity relationships observed in the original BOLD data. Voxels with similar BOLD signals would be expected to exhibit similar group-wise synchronization signals, but it is also possible that the group-wise synchronization signals, calculated across subjects, reveals functional connectivity relationships not observed at the within-subject BOLD level. To assess this question, we applied a temporal concatenation group ICA, at a lower model-order (n = 10) and higher model-order (n =100) solution, to the low-

Average BOLD Dynamics and Synchronization Comparison
Another important question is the extent that group-wise synchronization estimates are associated with across-subject task-driven increases or decreases in BOLD signals. In particular, Visual comparison of the average across-subject BOLD and the synchronization time courses from the first three components of each task (Figure 7) illustrates the relationship between these two signals. The BOLD and synchronization signals from the motor components exhibit similar temporal dynamics during large positive amplitude BOLD spikes in the data, corresponding to the onset of motor trials. The synchronization time courses of C1 from the theory of mind task, and C1 and C2 from the working-memory task also exhibit strong peaks in synchronization during large positive and negative amplitude bold spikes, respectively.
However, in time series with minimal BOLD amplitude spikes, such as the BOLD time courses of C2 and C3 from the theory of mind task, or low-BOLD amplitude periods in-between BOLD amplitude spikes, the correspondence between BOLD amplitude and synchronization time courses is reduced.
Studies of phase synchronization between broadband signals 67,68 , as the one used in this study (~0.01 to 0.085 Hz; this frequency range exhibited the strongest average synchrony across subjects), have demonstrated that synchronization estimates are more strongly correlated with synchronous large-amplitude signals spikes compared with lower-amplitude signal periods. This may explain the moderate relationship between average BOLD amplitude and group-wise synchronization estimates (r = ~ 0.3 -0.7). This property of broadband phase synchronization is beneficial as an exploratory approach, as synchronous high-amplitude BOLD spikes in the data are expected to be of more task-relevance compared with low-amplitude signal periods. In addition, a restricted broadband signal in the frequency range of 0.01 to 0.085 Hz was chosen to ensure that all possible task-driven signal dynamics within this commonly studied frequency range are detectable by the phase synchronization approach. As demonstrated in the results for all three tasks, this signal adequately captures task-driven signal dynamics.

Supplemental Experimental Procedures
The stationary wavelet transform (SWT) was implemented in the Inter-Subject Correlation (ISC) toolbox (21). The SWT is more desirable over standard implementations of discrete wavelet transforms, as it is time-invariant, making the filter bank construction robust to small differences in hemodynamic lag between participants that could lead to large inconsistencies in the estimation of inter-subject synchronization. The SWT algorithm operates through successive splitting of low pass-filtered signals into new low-and high-pass signals ( Figure S2. Of note, the SWT-filter is associated with a constant phase delay, and results in a constant 13 TR (6 sec) time delay for the filtered signal compared to the original signal. This time delay was compensated for by temporally shifting the standard GLM reference functions (discussed below).
The inter-subject eigenvalue synchrony approach was applied within each sub-band. The approach is conducted on a voxel-by-voxel basis and provides an assessment of group-wise synchrony in the time series across all subjects at each voxel. The eigenvalue synchrony analysis procedure is as follows: first, the pair-wise similarity between each pair of participants is calculated for every voxel in the brain (whole-brain voxel-by-voxel approach) by calculating the  (19,20,40) to calculating a group-wise synchrony estimate for each voxel, is to simply average across all pair-wise z-transformed correlation coefficients (essentially average the upper or lower triangle of the 75*75 participant correlation matrix). However, a more statistically principled way of estimating group-wise synchrony at each voxel that works over all participants simultaneously, and scales over sample size, would be to conduct an eigenvalue approach that estimates the first principle eigenvector and its associated eigenvalue through a singular value decomposition (SVD) of the participant-by-participant correlation matrix (18). The resulting eigenvalue is a measure of group-wise subject synchrony for that voxel, and ranges from 1 to the number of participants. The SVD algorithm provided through MATLAB was used to conduct this analysis. The strength of synchronization for each sub-band was computed by simply averaging the group-wise synchronization estimates across all voxels within the brain.
The resulting eigenvalue maps (representing eigenvalues at each voxel in the brain) were thresholded using the permutation testing framework implemented by Kauppi et al. (21), but adapted for constructing a null distribution of eigenvalues. Briefly, each participant's bandlimited time series is randomly circularly shifted so that participant time series are no longer aligned in time, and the first principle eigenvalue is computed, and this procedure is repeated 100,000 times to construct a null distribution of eigenvalues for each frequency band. P-values are computed for each voxel and then corrected for multiple comparisons using the false discovery rate (FDR; Benjamini and Hochberg, 1995).
In addition to determination of the strongest synchronization sub-band, the group-wise static synchronization estimates at each voxel across frequency sub-bands were compared with the 'activation' estimates (z-score estimates) derived from the standard GLM approach using the conventional reference function. In particular, static synchronization estimates for the motor, theory of mind and working memory task were spatially correlated with the absolute-valued all motor movement, theory of mind, and 2-back activation maps, respectively. This allowed for an assessment of the degree of correspondence between the identification of task-driven brain responses between the static inter-subject synchrony analysis and the standard GLM approach.