Endogenous variation in ventromedial prefrontal cortex state dynamics during naturalistic viewing reflects affective experience

The vmPFC ascribes affective meaning to experiences as they unfold and exhibits unique idiographic spatiotemporal dynamics.


INTRODUCTION
Our brains process complex information with incredible speed and efficiency. This information can be broadly categorized into two distinct classes. First, our brains directly process exogenous information about the external environment by transducing physical phenomena (e.g., changes in energy, molecular concentrations, etc.) into sensory perceptions that allow us to generate and maintain a sense of what is happening around us (1,2). Mental representations that are directly driven by the external world are likely to be highly similar across individuals who share the same sensory experience. Second, our brains also process endogenous information that reflects our current internal homeostatic states, past experiences, and future goals (3). The integration of exogenous and endogenous information allows us to meaningfully interpret our surroundings, prioritize information that is relevant to our goals, and develop action plans (4). Given the same input information, individuals may have unique interpretations, feelings, and plans, often leading endogenous representations to be idiosyncratic across individuals. How can we establish a broad functional commonality across individuals when these specific endogenous experiences may be unique to each individual?
This conceptual distinction between exogenous and endogenous processes may reflect an organizing principle of the brain. Recent work characterizing the functional connectomes of human and macaque brains has revealed topographic gradients from cortical regions that process exogenous information originating from a single sensorimotor modality (e.g., auditory, visual, and somatosensory/ motor) to transmodal association cortex such as the default mode network (DMN) (5,6). The DMN, which encompasses the ventromedial prefrontal cortex (vmPFC), posterior cingulate cortex (PCC), dorsomedial prefrontal cortex (dmPFC), and temporal parietal junction (TPJ), was initially identified to be metabolically active in the absence of any psychological task (7)(8)(9)(10)(11). Subsequently, the DMN has been linked to a number of endogenous processes such as engaging in spontaneous internal thought and mind wandering (12)(13)(14), thinking about the self (15,16), prospecting into the future (17,18), and recalling autobiographical memories (19)(20)(21).
Within the DMN, vmPFC responses are particularly variable across individuals. Voxels in this region show little evidence of temporal synchronization across individuals when listening to auditory stories (22) or watching movies (23,24). Moreover, decoding accuracy using pattern classification is generally lower in the vmPFC compared to unimodal sensory areas (25), and functional connectivity patterns in resting-state functional magnetic resonance imaging (fMRI) appear to be more variable across individuals in the vmPFC than in other areas of cortex (26,27).
Beyond an individual's unique appraisals, there are several potential methodological factors contributing to the variability of vmPFC responses across individuals. First, the vmPFC is particularly vulnerable to susceptibility artifacts due to its close proximity to the orbital sinus, which can increase noise due to signal dropout and spatial distortions. These artifacts can be slightly mitigated by optimizing scanning parameters and sequences (46)(47)(48). Second, because the vmPFC is transmodal and integrates information from parallel processing streams, there may be greater variability in the temporal response profile of this region. While all brain regions exhibit some form of temporal integration, the lengths of temporal receptive windows are thought to be hierarchically organized on the basis of levels of information processing (49,50). In early sensory regions, this integration occurs over short temporal receptive windows that reflect rapidly changing inputs. By contrast, regions involved in abstract processing (e.g., narrative comprehension) exhibit much longer temporal receptive windows (51)(52)(53). Together, this suggests that the heterogeneity observed in vmPFC signals arises from a combination of individual variability, spatial distortion, and temporal variation.
Establishing functional commonalities that transcend this variation in vmPFC response profiles requires identifying new ways to align signals across individuals. One such alignment procedure commonly used in the decision neuroscience literature uses an idiographic approach whereby experimental paradigms are customized to specific individuals (37,(54)(55)(56). On the basis of an individual's preferences, stimuli are mapped onto ordinal value signals, which are then used to identify brain regions that exhibit a linear correspondence (57). Another promising alignment approach attempts to remap regions across participants based on common temporal response profiles to the same time-locked external stimulation. Functional alignment algorithms such as Hyperalignment (58,59) and the Shared Response Model (SRM) (60) can be highly effective at improving spatial alignment across people based on common functional responses while still maintaining individual differences (61). This approach might be particularly well suited for improving alignment in regions that process exogenous information and also potentially useful for mitigating variability arising from spatial distortions. However, because vmPFC responses reflect idiosyncratic appraisals based on endogenous information that are far removed from the exogenous input stimuli (e.g., goals, memories, etc.), vmPFC activity patterns likely cannot be aligned across individuals in space or time using such approaches. Rather, aligning vmPFC responses across individuals might require developing a new approach that detects changes in latent states (e.g., mental and physiological).
In the present study, we investigate how the vmPFC processes endogenous information while viewing a rich naturalistic stimulus. Participants watched a 45-min pilot episode of a character-driven television drama [Friday Night Lights (FNL)] while undergoing fMRI. This show was chosen in particular for its engaging story arc, parallel plotlines, and range of dynamics in affective experiences. We test the hypothesis that vmPFC activity reflects changes in latent states associated with the interaction between exogenous and endogenous processes. These states are hypothesized to reflect appraisals of meaningful plot elements as a narrative unfolds (e.g., "that is amazing!" or "that is terrible!") that ultimately result in the emergence of feelings. More specifically, we predicted (i) greater heterogeneity in spatiotemporal dynamics in vmPFC across individuals relative to primary sensory regions, (ii) longer processing time scales in the vmPFC compared to primary sensory regions, and (iii) that changes in vmPFC states correspond to meaningful psychological experiences.

Idiosyncratic spatiotemporal dynamics of the vmPFC
We hypothesized that the vmPFC plays a critical role in processing endogenous information by integrating information from the external world with internal states, past experiences, and future goals. Unlike regions that directly process exogenous information (e.g., early visual cortex), we predicted that there should be little across-participant consistency in vmPFC responses during natural viewing. We tested this hypothesis using two separate studies. Participants in study 1 (n = 13) were scanned on a Philips 3T scanner while watching the first two episodes of FNL. Participants in study 2 (n = 35) were scanned on a Siemens Prisma 3T scanner while watching only the first episode of the same show. First, we examined consistency in temporal responses across the 45-min episode using intersubject correlations (ISCs; see Methods) (23). To reduce computational complexity, all analyses were performed on 50 nonoverlapping regions on the basis of a whole-brain parcellation using meta-analytic coactivations from over 10,000 published studies (62). We then computed the pairwise temporal similarity of mean activity within each parcel across all participants. This yielded a number of participantsby-number of participants correlation matrix for each of the 50 parcels. ISC is simply the average of these pairwise similarities across participants. In study 1, early sensory regions (e.g., V1) exhibited the highest level of temporal synchronization (mean ISC = 0.38, SD = 0.13, P < 0.001), whereas vmPFC showed little evidence of synchronization across participants (mean ISC = 0.06, SD = 0.07, P < 0.001; Fig. 1A). These results were replicated in study 2; V1 was associated with high levels of temporal ISC (mean ISC = 0.35, SD = 0.13, P < 0.001), whereas the vmPFC exhibited a low degree of synchronization (mean ISC = 0.07, SD = 0.05, P < 0.001; Fig. 1B). The overall spatial pattern of ISC across brain parcels was highly preserved across the two studies, r(48) = 0.99, P < 0.001.
Although vmPFC activity was idiosyncratic when considering the full duration of the episode, it is possible that activity might briefly align during particular moments of the episode. For example, an engaging pivotal moment in the story might evoke strong responses across individuals, whereas less salient moments might encourage person-specific endogenous processing. We defined a metric of instantaneous intersubject synchronization in study 1 using the average spatial ISC computed across patterns of voxel activity within each region of interest (ROI) during each time point [i.e., each repetition time (TR); see Methods]. Unlike other methods of dynamic synchrony, this approach does not require specifying a sliding window length or shape (63) or restricting the analysis to a specific temporal frequency band (64). Instead, it characterizes the average alignment of spatial activity patterns across participants. Across all time points, we observed a modest spatial ISC in sensory regions, such as V1 (mean ISC = 0.1, SD = 0.06; Fig. 1C) and virtually no synchronization in the vmPFC (mean r = 0.01, SD = 0.03; Fig. 1C). One possible explanation for these findings is that spatial distortions created from susceptibility artifacts might have increased variations in the spatial configuration of vmPFC voxels for each participant or, alternatively, that anatomical alignment techniques were insufficient for aligning fine-grain spatial patterns across individuals. For these reasons, we functionally aligned each region into a common 1000-dimensional space by fitting an SRM (60) to independent data (i.e., episode 2). Consistent with previous work, we found that functional alignment markedly improved spatial ISC across participants in regions involved in exogenous processing such as V1 (mean r = 0.25, SD = 0.19, P < 0.001; Fig. 1D) but had no appreciable impact on vmPFC synchronization (mean r = 0.02, SD = 0.04, P = 1.0; Fig. 1D) (58)(59)(60).
These results demonstrate that vmPFC activity patterns do not appear to align spatially or temporally across people, which could arise from at least two possible explanations. First, it is possible that incoming stimulus-driven information does not directly affect vmPFC activity. For example, the vmPFC might play a role in representing or driving endogenous thoughts that are specifically unrelated to the exogenous experience (e.g., mind-wandering). Alternatively, the vmPFC may be involved in representing information or thoughts related to the stimulus (e.g., appraisals), but this information may be idiosyncratic to each individual.

Temporal recurrence of spatial patterns
To more precisely characterize the structure of vmPFC responses across the episode, we examined the temporal recurrence of each individual's unique patterns of vmPFC activity. For each participant, we computed a number-of-time points by number-of-time points correlation matrix reflecting the similarity of spatial patterns of vmPFC activity over the 45-min episode. This analysis can aid in identifying time points during the show where a participant demonstrates a similar pattern of vmPFC activity, which might reflect a recurrence of a similar psychological state.
As shown in Fig. 2A, this temporal correlation matrix exhibited a notable block diagonal structure. Specifically, the vmPFC exhibited periods of stable activity that persisted up to several minutes, punctuated by moments of rapid change (see figs. S1 to S4 for all participants). This suggests that there are likely several different spatial configurations of vmPFC activity that are maintained for long periods of time. To determine whether these response profiles were consistent across participants, we computed a one-sample t test on Fisher z-transformed correlation values at each pair of time points across all participants (study 2, n = 35). After correcting for multiple comparisons, we found very few time points that exhibited a consistent recurrence structure across participants (Fig. 2B). Rather than treating each time point independently, we also examined whether the relative pattern of spatiotemporal dynamics was consistent across participants (i.e., the similarity of the lower triangles of the time × time  Temporal ISC for each ROI for study 2 (n = 35); same format as (A). (C) Spatial ISC across participants averaged across TRs for study 1. Spatial ISC reflects the pairwise spatial similarity of activity patterns across participants within each ROI at each TR. Functional alignment in the right subpanel was performed using the SRM (60) on an independent dataset. Parcels in which spatial ISC significantly increased following functional alignment are outlined in gray [estimated using a permutation test, false discovery rate (FDR) q < 0.05, which corresponds to P = 0.015]. (D) Spatial ISC at each TR across the 45-min episode for the vmPFC and V1 ROIs for study 1. Lighter colors denote anatomical alignment of voxels across participants. Darker colors denote functional alignment. spatial similarity matrix) (Fig. 2C) and found little evidence of spatiotemporal synchronization (mean r = 0.03, SD = 0.01). In comparison, we observed a modest but reliable spatiotemporal synchronization across participants in V1 (mean r = 0.12, SD = 0.07; Fig. 2C, bottom) and a low spatial correlation in PCC (mean r = 0.05, SD = 0.03; fig. S11B). Together, these results indicate that participants appear to share a block diagonal structure revealing long periods of sustained vmPFC activity, but the specific dynamics and patterns of recurrence appear to be idiosyncratic to each individual participant.

The vmPFC has a long temporal autocorrelation function
To quantify the rate of temporal integration of information in the vmPFC, we estimated the temporal autocorrelations of activity throughout the brain (50). Specifically, we estimated the amount of autocorrelation for each individual voxel in the brain up to 50 TR lags. We then fit an exponential function to the mean of these estimates within each ROI using a robust estimator and calculated the number of time points before the function decayed to an arbitrary threshold of 0.1 (see Methods). Figure 3A illustrates the estimated amount of autocorrelation at the voxel level across each of the 50 parcels. Using a nonparametric sign test, we found that the autocorrelation in voxels in the vmPFC took longer to decay compared to V1 in both study 1 (vmPFC, mean = 18.46 TRs, SD = 6.6 TRs; V1, mean = 3.62 TRs, SD = 1.19 TRs, P < 0.001) and study 2 (vmPFC, mean = 8.46 TRs, SD = 2.95 TRs; V1, mean = 3.8 TRs, SD = 1.21 TRs, P < 0.001). Additional supplementary analyses revealed that vmPFC voxels with longer autocorrelation were associated with a lower temporal signal-to-noise ratio (tSNR), indicating that this effect may be partially attributed to susceptibility artifacts (study 1, r = −0.72; study 2, r = −0.71). However, susceptibility artifacts could not fully account for our findings, as we still observed a reliable distribution of voxel autocorrelation in the vmPFC across studies 1 and 2 after removing study-specific tSNR variance, r = 0.58 (see fig. S5).
Next, we sought to evaluate whether the multivoxel spatial pattern within each ROI might be integrating information over a longer time window. We applied the same autocorrelation estimation procedure used above using the multivoxel pattern within each ROI. We found that the vmPFC displayed much more gradual changes in pattern responses compared to sensory regions such as V1 for both study 1 (vmPFC, mean = 21.69 TRs, SD = 8 TRs; V1, mean = 4 TRs, SD = 1.47 TRs, P < 0.001) and study 2 (vmPFC, mean = 10.57 TRs, SD = 4.13 TRs; V1, mean = 4.06 TRs, SD = 1.63 TRs, P < 0.001). Although we observed that the autocorrelation was longer for the vmPFC compared to V1 for both single voxels and spatial patterns, only vmPFC patterns exhibited a significantly longer autocorrelation compared to the average voxel autocorrelation for both study 1 (vmPFC, P = 0.003; V1, P = 0.12) and study 2 (vmPFC, P < 0.001; V1, P = 0.08). This suggests that information encoded in spatial patterns in the vmPFC is being integrated over longer periods of time than sensory regions. Unlike previous work that has demonstrated similar findings by causally manipulating presented information at different temporal scales (e.g., scrambling words, sentences, or paragraphs) (22,51), this method allows us to estimate the longevity of spatial patterns within an ROI in a context-general way (including nonstimulus-driven contexts) similar to exploring variations in power spectra (52,53,65,66).

Spatial alignment of vmPFC latent states
The ISC analyses described above establish that the vmPFC does not show consistent responses across participants in its average time course or spatial patterns using either anatomical or functional alignment. Our temporal recurrence analysis revealed that each participant exhibited a similar block diagonal structure characterized by long periods of sustained vmPFC activity that recurred at multiple points throughout the episode. This suggests that the vmPFC may slowly transition between different states. Although the overall patterns of recurrence did not appear to synchronize across participants, it is possible that a subset of these states might be shared across participants but expressed at different moments in time. To test the hypothesis that participants exhibit shared states at different times, we used hidden Markov models (HMMs) to segment patterns of activations in the vmPFC into discrete latent states. In implementing this analysis, we made several simplifying assumptions to gain traction. Specifically, we assumed that (i) voxel activations were drawn from orthogonal Gaussian distributions, (ii) the transitions in latent states had the form of a first-order Markov chain, and (iii) all participants experienced the same number of states. For each participant, we fit a separate HMM to a set of orthogonal principal components that explained 90% of the variance of the participants' multivariate vmPFC time series. We used the Viterbi algorithm (67) to determine the probability that the participant was in a particular state at each moment of viewing the episode (Fig. 4A) and aligned the states across participants by maximizing the spatial similarity using the Hungarian algorithm (68). To determine the number of states for the HMM estimation procedure, we identified the number of states that maximized the average within-state spatial similarity relative to the average between-state similarity. Overall, we found that a low number of states (k = 4) appeared to yield the highest average within-state to between-state spatial similarity for vmPFC across both studies 1 and 2. We observed a slightly higher number of states for V1 for study 1 (k = 6) and study 2 (k = 7) and a large number of states for PCC for study 1 (k = 17) and for study 2 (k = 12) ( fig. S9). In contrast to the spatial ISC analyses, the individual-HMM analysis revealed that a subset of the latent vmPFC states appeared to be shared across participants (Fig. 5A). The state with the highest spatial consistency in vmPFC and V1 is depicted in Fig. 5B, and the corresponding spatial patterns averaged across participants are shown in Fig. 5C. The magnitude of the HMM spatial similarity is in the upper range of what we observed in our spatial ISC analyses after performing functional alignment.
Next, we examined whether these latent states exhibited any temporal consistency using a concordance metric, which we defined as the proportion of participants occupying a given state at each moment of the episode. We plot the overall concordance of the vmPFC and V1 states that exhibited the highest spatial consistency across time in Fig. 5D. This analysis indicates moderate state concordance in vmPFC (study 1, mean = 0.25, SD = 0.12; study 2, mean = 0.25, SD = 0.08) and V1 (study 1, mean = 0.16, SD = 0.11; study 2, mean = 0.15, SD = 0.06), but small levels of state concordance for PCC, presumably because of the larger number of states (study 1, mean = 0.05, SD = 0.06; study 2, mean = 0.08, SD = 0.04; fig. S11) (see tables S1 and S2 for all states). The time courses of these state concordances appear to show some degree of consistency across studies. We observed a moderate correlation in the temporal concordance between studies 1 and 2 for V1 [r(1362) = 0.24, P < 0.001], a small correlation for vmPFC [r(1362) = 0.05, P = 0.07], and no significant correlation for PCC [r(1362) = −0.03, P = 0.23]. Together, these analyses suggest that while it is possible to identify consistent spatial patterns in the vmPFC for specific states, these states tend not to be occupied by the same participants at the same moments in time (except at a few specific time points-i.e., local maxima in Fig. 5D).

Shared latent states using group-HMM
The individual-HMM analyses revealed that participants exhibited similar brain patterns for each latent state but rarely occupied these states at the same moments in time. Building on these results, we estimated a group-HMM for all participants in each study treating each participant as an independent sequence (69 Spatial pattern similarity matrix We plot the average aligned transition probabilities for study 2. We then applied the model to the same data to predict the most likely latent state at each moment in time using the Viterbi algorithm. (B) We aligned states across participants by maximizing the spatial similarity of the Gaussian emission weights associated with each estimated state using the Hungarian algorithm.
within each study but allows each participant to have a unique sequence of states. We selected the number of states in which the Bayesian information criterion (BIC) (70) exhibited the largest improvement over a range of states (i.e., k = [2, 25]; fig. S10). Similar to the analysis performed on each individual participant, this procedure identified a low number of states for both studies 1 and 2 (k = 4). The transition probability matrices can be viewed in fig. S9. We were also interested in the generalizability of the states we identified across other contexts. For example, when participants in study 1 watched the second episode, did they exhibit a similar set of states to those we identified while they watched the first episode? (Participants in study 2 only watched a single episode.) To address this question, we trained an additional k = 4 group-HMM on the vmPFC data collected while study 1 participants viewed the second FNL episode. We aligned the states from the models trained on each episode using the Hungarian algorithm (68) and assessed the crossepisode state concordance synchronization using Pearson correlations ( fig. S8). Overall, we found that three of the four states appeared to be capturing similar states when testing the models on episode 1 (state 1, r = 0.3, P < 0.001; state 2, r = 0.64, P < 0.001; state 3, r = 1.0, P = 0.001; state 4, r = −0.03, P = 0.29; fig. S8A) and episode 2 (state 1, r = 0.3, P = 003; state 2, r = 0.71, P = 0.002; state 3, r = 1.0, P < 0.001; state 4, r = 0.01, P = 0.93; fig. S8B) using a circle-shifting permutation test. These results provide evidence demonstrating that the vmPFC states estimated from a single viewing episode appear to generalize to other episodes. vmPFC state concordance is associated with affective experience The above results demonstrate that participants exhibited similar spatial representations in the vmPFC based on the emission patterns associated with each latent HMM state. However, the time courses of how these patterns are expressed appear to be considerably less consistent across participants. We next sought to understand what types of thoughts or processes might be reflected by these vmPFC states.
We first performed a reverse correlation analysis (23) to identify which scenes from the show corresponded to the periods of high across-participant state concordance (Fig. 6A). We found that high  5. Alignment of spatial patterns corresponding to latent states. In this figure, we illustrate that the spatial patterns estimated from each individual HMM appear to be shared across participants. (A) We plot the spatial similarity of the emission patterns corresponding to each individual's state after aligning the states across participants using the Hungarian algorithm. The outlines indicate patterns associated with each participant for a given state in vmPFC and V1 in study 1 (n = 13) and study 2 (n = 35). We highlight the vmPFC and V1 states with the highest intersubject spatial similarity (blue, study 1; red, study 2). (B) We plot the magnitude of the spatial similarity for the states with the highest overall spatial similarity highlighted in (A) averaged across participants. (C) We plot the vmPFC and V1 spatial patterns that correspond to the states associated with the highest intersubject spatial similarity from studies 1 and 2. These maps reflect the emission probabilities associated with each state averaged across participants. (D) Temporal concordance of the highlighted predicted states across individuals within each study. Higher values indicate a higher proportion of participants occupying the same putative latent state within each study (blue, study 1; red, study 2).
concordance intervals occurred during scenes with strong narrative importance for the episode. These key moments include scenes such as when the football players serve as mentors to young kids (~22 min), the protagonist is severely injured (~35 min), and the backup quarterback leads the team to an unexpected victory despite the setbacks (~42 min). Further, these states appear to be maintained for durations on the order of multiple minutes and are consistent across different participants and scanners.
To gain further quantitative insight into the identified vmPFC states, we collected two additional behavioral datasets to identify the facial expression behaviors and subjective self-reported feelings evoked by the television show in independent samples of participants. In study 3, participants (n = 20) watched the first episode of FNL while their facial expressions were video recorded (71). We used a computer vision algorithm to identify 20 facial action units (AUs), a standardized system to describe the intensity of facial muscle movements (72), for each frame of the video during the episode (73). In study 4, we recruited participants (n = 188) from Amazon Mechanical Turk to watch the same television episode, which was periodically paused at 12 randomly selected time points spanning the episode, so that participants could report their subjective feelings on 16 different emotional dimensions. A different set of time points was chosen for each participant. We then used a collaborative filtering (CF) technique based on nonnegative matrix factorization (see Methods) to predict how each participant was feeling for the remaining time points across all 16 dimensions.
We estimated a cross-experiment SRM (60) to identify a common latent space shared across all four experiments. This entailed learning study-specific transformation matrices that projected the following time series into a shared latent space: (i) the study 1 4-dimensional  vmPFC HMM state concordance time series, (ii) the study 2 4-dimensional vmPFC HMM state concordance time series, (iii) the average study 3 20-dimensional facial expression AU time series, and (iv) the average study 4 16-dimensional self-reported subjective emotion rating time series. The time course for each latent state was consistent across studies for all four states (mean ISC = 0.23, SD = 0.03), and in the moderate range we observed for temporal ISC across the entire brain. The latent time series can be observed in Fig. 6A and indicates a clear differentiation of signals at the three highlighted scenes. States 2 and 3 increase when the star quarterback experiences a traumatic spinal cord injury and undergoes emergency surgery (~35 min), while state 1 increases when the nervous and inexperienced backup quarterback throws an impressive pass that allows the team to come back and win the big game (~42 min). These latent state time series capture the reliable changes in vmPFC HMM state concordance across both studies 1 and 2. However, we can also use the transformation matrices from studies 3 and 4 to directly interpret affective processes associated with these latent components (74). In Fig. 6B, we project the transformation matrices back to AUs to visualize the facial expressions displayed by participants in study 3 at these particular time points (see also fig. S16). State 1 is most associated with increased intensity of AU12 (zygomaticus major; intensity = 2.86), AU14 (buccinator; intensity = 3.36), and AU24 (orbicularis oris; intensity = 4), which presses the lips together and pulls the lip corners to form a smile (75). State 2, in contrast, is most associated with raising the eyebrows (AU1; frontalis, pars medialis; intensity = 3.11; and AU2; frontalis pars lateralis; intensity = 3.34), depressing the lip corners (AU15; depressor anguli oris; intensity = 3.09), raising the chin (AU17; mentalis, intensity 3.27), and funneling the lips (AU18; incisivii labii superioris; intensity = 4.0). This suggests that vmPFC state 1 is associated with feelings of positive affect, whereas state 2 is associated with a feeling of surprise, concern, or worry. We visualized the transformation matrices from study 4 using word clouds. Consistent with these interpretations of the facial expression behaviors, we found that the top five feelings associated with state 1 included hope, pride, fear, joy, and satisfaction, while the top five feelings associated with state 2 included sadness, fear, hope, interest, and guilt ( fig. S17). Together, our results indicate that participants collectively experienced at least two latent affective states while watching the episode, with our interexperiment latent state model providing convergent evidence for distinct representations for positive and negative valence. When more participants from studies 1 and 2 occupied state 1 based on their vmPFC patterns, participants in studies 3 and 4 were smiling and experiencing positive feelings. In contrast, when more participants in studies 1 and 2 occupied state 2 based on their vmPFC patterns, participants in studies 3 and 4 were expressing and experiencing sadness and fear. This suggests that vmPFC states are linked to exogenous inputs and are more likely to align across individuals in contexts that elicit more intense affective responses (4,33,76).
These findings appear to be fairly specific to increased state synchronization in the vmPFC. vmPFC state 1 concordance increased at the same time points that participants smiled and subjectively reported feeling joy, while state 2 concordance increased when participants frowned and reported feeling sadness ( fig. S13). V1 state concordance, in contrast, did not appear to be particularly coupled with changes in affect but rather coupled strongly with large decreases in visual luminosity ( fig. S12). State concordance in other transmodal regions such as the PCC also did not appear to be strongly connected to affective experiences ( fig. S14). More detailed feature mapping to time periods of high state concordance can be viewed in fig. S15.

Endogenous brain activity associated with each vmPFC state
To provide additional insight into the psychological states associated with each vmPFC state, we computed whole-brain univariate contrasts based on when the group-HMM identified each participant's vmPFC to be in a particular state. These analyses are identical to traditional task-based univariate contrasts (77), but rather than identifying epochs based on manipulated experimental conditions, we used idiographic vmPFC state occupancy. That is, we identified average brain activity that increased during time points when individual vmPFCs are in a specific state. These time points vary across each individual, which means that these time points are locked to similar endogenous psychological states rather than exogenous events evoked by the stimulus. We used meta-analytic decoding using the Neurosynth framework to provide quantitative reverse inferences for each map (see fig. S18) (78,79). State 1 was associated with increased activity in the dorsal anterior cingulate (dACC), bilateral insula, bilateral, amygdala, and bilateral nucleus accumbens. These regions are associated with reward, fear, pain, motor, and somatosensory processing consistent with previous work characterizing positive valence in naturalistic films (80). State 2 was associated with increased activity in the vmPFC, PCC, dmPFC, TPJ, and superior temporal sulcus consistent with naturalistic work investigating negative affective experiences (81). These regions comprise the default mode and are associated with social processing. State 3 is associated with increased activity in the dACC and dorsal anterior insula. These regions are part of the salience network and are associated with executive control, attention, conflict, and learning. No voxels survived multiple comparisons correction for state 4. All contrasts are available on Neurovault (https://neurovault.org/collections/9062/).

DISCUSSION
In this study, we investigated how the vmPFC processes information while viewing a rich, evocative, and multimodal naturalistic stimulus. We found evidence that the spatiotemporal response profiles of the vmPFC were heterogeneous across individuals, even after applying spatial and temporal alignment algorithms to the data. However, we also found that individual vmPFC spatial patterns appeared to persist for long periods of time and that these patterns were periodically revisited over the course of the episode. The long window of temporal integration in the vmPFC was present in individual voxels but was enhanced in the spatial patterns. We used HMMs to segment patterns of vmPFC activity into discrete latent states and found that a subset of these states appeared to be shared across individuals. Although these states were most often expressed at different moments in time across individuals, scenes that evoked strong affective responses appeared to synchronize these latent states across participants, a finding which replicated in an independent sample collected on a different scanner. Moreover, we observed converging evidence that these states synchronized with specific interpretable patterns of facial expressions and subjective affective ratings in two additional independent samples viewing the same television episode outside of the scanner. Together, these vmPFC activity states appear to reflect latent endogenous psychological processes involved in conferring affective meaning to ongoing events. This helps to explain the heterogeneity of vmPFC responses across people and also has implications for experiments designed to probe the function of this region.
The vmPFC appears to be broadly involved in making meaning of the external world (3,4). It has been associated with representing and navigating cognitive maps and conceptual spaces (82)(83)(84) and interpreting narratives (41,42,45,66), which often requires abstracting temporal structure of abstract models of situations (44). At its most basic level, making a simple evaluation about the valence of an object or event (i.e., is it good or bad?) requires making an interpretation based on an individual's past experiences, current homeostatic states, and future goals. This appraisal process appears to be directly linked to the vmPFC (35,37). For example, evaluating a particular food option requires integrating multiple features such as taste, cost, and caloric content (85) with broader goals such as eating healthy (86) and internal homeostatic drives (87). Beyond food, the vmPFC appears to code general representations of subjective valence appraisals that transcend stimulus modalities (33,88,89). Countless studies have implicated the vmPFC in processing the valence of emotional memories (32) and chemosensory olfaction (90,91) and gustation (56) signals. These types of affective experiences of feelings, smells, and tastes can be causally induced with direct electrical stimulation of this region via intracranial electrodes implanted in patients with epilepsy (34). In this study, we find the highest level of synchronization of vmPFC states at the most emotionally evocative narrative events, which is consistent with work using pupillometry (76) and fMRI (80,81), indicating that people temporally synchronize mental states at affectively arousing events.
Extracting meaning from our subjective experiences requires integrating multimodal information at a variety of time scales. Consistent with work that has demonstrated a cortical hierarchy of processing temporal information (22,49,51,65), we find that the vmPFC maintains stable states over time scales on the order of tens of seconds to minutes. While this slow processing is represented to some extent in the autocorrelations of individual voxels, it becomes more apparent when examining temporal autocorrelations of spatial patterns (92). Our autocorrelation approach complements experimental designs that shuffle information at multiple time scales (22,51). While most methods studying neural processes have focused on studying fast signals that are closer to the firing of individual neurons, fMRI may be particularly well suited for studying slower signals that involve integrating information across time such as the transformation of experience into memories (24,93).
One set of questions that our study does not resolve concerns how the representations supported by the vmPFC change over time. Our autocorrelation analyses (e.g., Fig. 3) suggest that vmPFC activity patterns tend to change relatively gradually. However, our analyses of the temporal recurrences of spatial patterns in the vmPFC (e.g., Fig. 2) and our HMM-based analyses (e.g., Figs. 4 to 6) suggest that the vmPFC exhibits periods of relative stability (what we refer to as states) punctuated by moments of relatively rapid change (i.e., state transitions). Because state transitions do not occur instantly and identifying when state transitions occur is an inherently noisy process, our analyses cannot distinguish whether the vmPFC is best characterized as gradually drifting or state-like. Hybrid models that integrate both continuous and discrete processes [e.g., (94,95)] may be better suited to teasing apart these possibilities in future work. What we can conclude from the current results is that patterns of vmPFC activity appear to fluctuate over time. Although the spatial configuration of these patterns appears to be shared across participants, participants rarely appear to be expressing these patterns at the same precise moments.
Overall, we find that participants exhibit unique spatiotemporal response patterns in the vmPFC while viewing the same television episode. Our findings demonstrate that this cannot be solely accounted for by measurement issues (e.g., susceptibility artifacts and variations in hemodynamic response functions). These results present a significant challenge to traditional neuroimaging analysis methods that assume a common response profile across participants [e.g., two-level univariate analyses (96), resting-state analyses (97), multivariate pattern analysis approaches (98,99), intersubject synchrony (23,41,100), and functional alignment (58)(59)(60)]. Because subjective endogenous experiences are not typically shared across participants, regions like the vmPFC that appear to exhibit idiosyncratic stimulus-driven activity may be mischaracterized by these approaches. Our state-based analysis framework provides a means of characterizing this endogenous stimulus-driven activity, even when the response patterns do not align spatially or temporally across individuals, or to the external stimulus. Our approach may also be useful in translational applications where patient groups are often highly heterogeneous compared to healthy controls.
We note several limitations of our work. First, we assume that the anatomical demarcation of the vmPFC is consistent across all participants. We used a large ROI that was defined by a meta-analytic coactivation-based parcellation (62). However, the vmPFC can be further subdivided into more functionally specific regions (29), each which may have a unique response profile. We note that our patternbased approach leverages variability across these subregions to identify state changes. Second, our HMM analyses assume that all participants experience the same number of latent states while viewing the television episode. This assumption was necessary to constrain the model and to evaluate spatial and temporal consistency across participants. However, it is unlikely that there is a ground truth "correct" number of states or that all participants experience the same number of states. Last, we do not directly link emotional experiences to vmPFC activity within a single participant. Instead, we provide converging evidence across different studies that are time-locked to the stimulus presentation. Video measurements of facial expressions while scanning are difficult because of occlusions from the head coil. However, simultaneous facial electromyography with fMRI has shown promise by demonstrating a relationship between displays of negative affect via facial expression and vmPFC activity (101) and may provide an avenue for future work.
In summary, we find evidence indicating heterogeneity in exogenous and endogenous information processing across the brain. The vmPFC appears to be involved in ascribing meaning to ongoing experiences with respect to the unique endogenous thoughts individuals bring to bear on processing each new moment. These processes may be reflected in spatial patterns (78,(102)(103)(104)(105), which appear to be unique to each appraisal and experience and change at relatively slow time scales. We observe increased synchronization of these spatial patterns at emotionally salient scenes (76), suggesting that manipulating internal states (e.g., homeostatic states, memories, goals, or feelings) can increase vmPFC response synchrony across individuals. Our work demonstrates the potential of characterizing the temporal dynamics of spatial patterns to study the experiences of a single individual elicited during naturalistic multimodal scanning paradigms.

Study 1 Participants
Thirteen participants (mean [SD] age = 24.61 [4.77]; six female) were undergraduate and graduate students at the Dartmouth College participating for either monetary compensation ($20/hour) or for partial course credit. All participants gave informed consent in accordance with the guidelines set by the Committee for the Protection of Human Subjects at the Dartmouth College. Procedure Participants completed two separate sessions. In the first session, participants watched episodes 1 and 2 of the television drama FNL while undergoing fMRI. This show was chosen in particular for its engaging story arc, parallel plotlines, and range of affective experience dynamics. We scanned two separate episodes to ensure that we had sufficient data to perform functional alignment on independent data. Participants viewed each episode with a break in between, followed by two runs of passively viewing images of characters. In a second session, participants watched episodes 3 and 4 outside of the scanner while we recorded their facial expressions using a headmounted camera. All episodes were approximately 45 min in length. After each episode, participants made ratings of characters on a computer. The character viewing session, facial expressions of episodes 3 and 4, and the character ratings will be discussed in more detail in forthcoming manuscripts; those data are not reported in the present manuscript.

Imaging acquisition
Data were acquired at the Dartmouth Brain Imaging Center (DBIC) on a 3T Philips Achieva Intera scanner (Philips Medical Systems, Bothell, WA) with a 32-channel phased-array SENSE (sensitivity encoding) head coil. Raw images were saved directly to NIfTI format. Structural images were acquired using a high-resolution T1-weighted three-dimensional turbo field echo sequence: repetition time (TR) = 8200 ms, echo time (TE) = 3.7 ms flip angle = 8°, resolution = 0.938 mm by 0.938 mm by 1.00 mm voxels, matrix size = 256 by 256, and field of view (FOV) = 240 mm by 240 mm. Functional blood oxygen level-dependent (BOLD) images were acquired in an interleaved fashion using single-shot gradient-echo echo-planar imaging with prescan normalization, fat suppression, and an in-plane acceleration factor of two (i.e., SENSE 2): TR/TE = 2000/30 ms, flip angle = 75°, resolution = 3 mm 3 isotropic voxels, matrix size = 80 by 80, and FOV = 240 mm by 240 mm, 40 axial slices with full brain coverage and no gap, anterior-posterior phase encoding. Functional scans were acquired during each episode in a single continuous run per episode (episode 1, 1364 TRs; episode 2, 1317 TRs).

Study 2 Participants
Thirty-five participants (mean [SD] age = 19.0 [1.07] years; 26 female) were recruited from undergraduate introductory psychology and neuroscience courses for either course credit or monetary compensation at the Dartmouth College. All participants gave informed consent in accordance with the guidelines set by the Committee for the Protection of Human Subjects at the Dartmouth College.

Procedure
The experimental procedure was identical to study 1, with the exception that each participant only watched the first episode of FNL (45 min) while undergoing fMRI. This dataset provides a larger sample size on a different scanner to assess the replicability of our results.

Imaging acquisition
Data were acquired at the DBIC on a 3T Siemens Magnetom Prisma scanner (Siemens, Erlangen, Germany) with a 32-channel phased-array head coil. Raw DICOM images were converted to NIfTI images and stored in the brain imaging data structure format (BIDS) (106) using ReproIn from the ReproNim framework (107). Structural images were acquired using a T1-weighted, single-shot, high-resolution MPRAGE sequence with an in-plane acceleration factor of two (i.e., GRAPPA 2) and prescan normalization: TR/TE = 2300/2.32 ms, flip angle = 8°, resolution = 0.9 mm 3 isotropic voxels, matrix size = 256 by 256, and FOV = 240 mm by 240 mm. Functional BOLD images were acquired in an interleaved fashion using gradient-echo echo-planar imaging with prescan normalization, fat suppression and an in-plane acceleration factor of two (i.e., GRAPPA 2), and no multiband (i.e., simultaneous multislice) acceleration: TR/TE = 2000/25 ms, flip angle = 75°, resolution = 3 mm 3 isotropic voxels, matrix size = 80 by 80, and FOV = 240 mm by 240 mm, 40 axial slices with full brain coverage and no gap, anterior-posterior phase encoding. All functional scans were acquired in a single continuous run (1364 TRs).

Imaging preprocessing
All MRI data for both studies 1 and 2 were preprocessed using a custom pipeline written using Nipype (108). The pipeline involved trimming the first five nonsteady-state TRs of functional each scan using NIPY (109) and subsequently realigning each functional volume to the mean functional volume in a two-pass procedure implemented via FSL's MCFLIRT (110). In parallel, brain extraction (i.e., skull stripping) was performed on T1-weighted structural images using ANTS (advanced normalization tools) (111). Subsequently, transformations for linearly coregistering realigned functional volumes to skull-stripped structural images, and nonlinearly normalizing skull-stripped structural images to the ICBM 152 2-mm MNI template were calculated using ANTS. These transforms were then concatenated and applied in a single step using basis spline interpolation in ANTS. Data were spatially smoothed using a 6-mm full width at half maximum Gaussian kernel implemented using fslmaths (112). To perform denoising, we fit a voxel-wise general linear model (GLM) for each participant using custom software implemented in Python (https://github.com/cosanlab/ nltools). We used this toolbox to remove variance associated with the mean, linear, and quadratic trends, mean activity from a cerebral spinal fluid mask, the effects of motion estimated during the realignment step using an expanded set of 24 motion parameters (six demeaned realignment parameters, their squares, their derivatives, and their squared derivatives), motion spikes between successive TRs identified using Artifact Detection Tools (ART) (113), and global signalintensity spikes greater than three SDs above the mean intensity between successive TRs. All analyses occurred on the residual time series after GLM estimation. Code for this custom pipeline is available at https://github.com/cosanlab/cosanlab_preproc. Parcellation All imaging analyses were conducted over a set of 50 parcels (parcellation available at http://neurovault.org/images/39711). The parcellation was created by performing a whole-brain parcellation of the coactivation patterns of activations across over 10,000 published studies available in the Neurosynth database (62). The use of a parcellation scheme has several advantages over the more conventional voxelwise and searchlight approaches (114). First, it is several orders of magnitude less computationally expensive as analyses are performed only 50 times compared to 352,000 voxels. Second, the parcels are nonoverlapping and contain bilateral regions that reflect functional neuroanatomy, whereas a searchlight approach is limited to local spheres that do not adapt to different areas of cortex.

Intersubject correlation
We take the ISC to be the mean of the lower triangle of the pairwise correlation matrix of signals between each participant [see (115) for a tutorial] where is the Fisher z-transformation and is its inverse. S is a matrix of subject time series data from a total of N participants, and i and j indicate the subject indices. We performed hypothesis tests using a subject-wise bootstrap procedure as recommended by (116), which randomly draws participants with replacement to create a new sample by sample similarity matrix. Correlations between the same participants are dropped before computing ISC. We computed ISC for each participant's mean vmPFC time series, their vmPFC spatial pattern at each moment in time, and their unique spatiotemporal pattern, defined as the vectorized lower triangle of the participant's spatial recurrence matrix across all voxels in their vmPFC. We also carried out an analogous series of calculations with each participant's V1 activity patterns. The similarity of spatiotemporal patterns has an interesting connection to computing distance correlation (117,118), a measure of general (i.e., possibly nonlinear) statistical dependence between two signals of arbitrary dimensionality.

Functional alignment
We performed functional alignment on study 1 using the SRM (60). The deterministic SRM algorithm performs a joint Principal Components Analysis (PCA) and can identify a reduced set of functional response components that maximally align across participants. We chose an arbitrarily selected 1000-dimensional embedding for each ROI. This algorithm learns a separate transformation matrix that projects each participant into this common space (60). Estimating a lower-dimensional common model space can potentially aid in filtering out measurement noise that is assumed to be independent across individuals. To minimize bias and ensure that ISC analyses were estimated independent of computing the SRM (58), we learned transformation matrices using data from episode 2 and subsequently applied these transformations to data from episode 1. This allowed us to project each ROI's voxel responses into the common 1000-dimensional space. To identify regions where spatial ISC significantly improved as a result of functional alignment, we performed a paired-sample sign permutation test on the dynamic ISC value using 5000 samples and used a threshold of false discovery rate (FDR) q < 0.05 to correct for multiple comparisons.

Temporal recurrence of spatial patterns
We created a spatial recurrence matrix by taking the pairwise Pearson correlation of the vectorized vmPFC activity for each TR collected during the 45-min episode. This results in a number-of-TRs by number-of-TRs matrix (n = 1364 TRs) reflecting the degree to which the spatial activity patterns in the vmPFC are correlated at each pair of TRs. Sequential TRs where the spatial configuration of the vmPFC persists create a block diagonal structure. Recurring activity patterns at distant time points are reflected in the off-diagonal similarity.

Autocorrelation
To compute the autocorrelation function at each voxel, we calculated the average correlation of a voxel's activation time series with itself shifted by a lag of t time steps, for t ∊ {1, 2, …, 50}. This resulted in a correlation coefficient for each lag, for each voxel. We summarized the overall shape of this function within each ROI by taking the median across all voxels within the ROI and fitting a three-parameter exponential function using a robust estimator. The parameter estimation was performed by minimizing the residual sum of squared error using the curve_fit() function from the SCIPy toolbox (119). We used the median of the distribution of autocorrelation across participants to ensure robust parameter estimation where A is the median autocorrelation function. We used a similar procedure to calculate autocorrelation in spatial patterns. For each ROI, we computed a spatial recurrence matrix by correlating the activity patterns of each time t with the pattern at time t + lag, for lag ∊ {1, 2, …, 50}, and then averaging the matrices created for each time point. We fit an exponential function to the diagonal of the across-participant average spatial recurrence matrix.
To compare autocorrelations across ROIs, we calculated the number of TRs that the estimated exponential function took to reach an arbitrary correlation threshold of 0.1. This metric provides an intuitive and interpretable value for comparing the activity drift rates across regions and modalities (e.g., voxel versus spatial patterns) (50).

Hidden Markov model
To identify state changes reflected in the neural dynamics within the vmPFC, we fit HMMs to the voxel time series (120,121). HMMs are generative probabilistic models that propose that a sequence of observations is generated by a sequence of latent states. The transitions between these latent states are assumed to form a first-order Markov chain, such that the likelihood of transitioning to a new state from the current state can be predicted solely from the most recent data. We also assume that the observations are drawn from a multivariate Gaussian distribution with a diagonal covariance matrix. We performed two separate model fitting procedures: (i) an individual-HMM where a model is fit separately to each participant's data and (ii) a group-HMM where a single model is fit to all participants as a separate sequence.
First, we fit a separate HMM individually to each participant's voxel pattern time series (vmPFC = 3591 voxels; V1 = 2786 voxels). We reduced the dimensionality of the data using PCA and retained enough components to explain 90% of the variance in the original signal (65). Reducing the dimensionality reduced computation time, decreased noise, and allowed us to better meet the orthogonality assumptions of the diagonal covariance matrix for the emission probabilities. The vmPFC had a higher number of components in both study 1 (mean = 58.34.43, SD = 7.1) and study 2 (mean = 68.4.43, SD = 15.74) compared to V1 in study 1 (mean = 33.69, SD = 5.0) and study 2 (mean = 28.0, SD = 6.42). We then fit the HMM using the Gaussian HMM function from the Python hmmlearn package (version 0.2.4; https://github.com/hmmlearn/hmmlearn), which estimates the model parameters using expectation-maximization. We used the fitted models to compute the Viterbi sequence of states for each participant. We estimated a model for each participant over a range of k = [2,25]. For each model, we aligned the latent states of the participants to a randomly selected reference participant by maximizing the spatial correlation similarity between the estimated feature models using the Hungarian algorithm (68). We then selected the optimal value of k that maximized the average within state pattern spatial similarity relative to the between state pattern spatial similarity. This analysis demonstrated that participants shared similar patterns of activity in vmPFC associated with each state, but these patterns were not expressed at the same moments in time.
Second, we fit a single group-HMM model to all of the participants for each study by treating each participant's voxel pattern time series as an independent sequence (69). This procedure learns a single voxel emission pattern for each state across all participants but allows each participant to vary in the temporal sequence in the expression of the states. Because we cannot assess the spatial similarity of the emission patterns across participants as we did in the previous analysis, we selected the optimal number of states using the BIC (70). The BIC is a metric of model fit that penalizes the likelihood function for larger numbers of parameters to reduce overfitting defined as where n is the number of observations, k is the number of states, f is the number of features after reducing the dimensionality of the voxels using PCA, and ˆ L is the maximized log likelihood of the HMM model given the data. Similar to the analyses above, we fit an HMM with Gaussian emissions assuming diagonal covariance to the principal components that explain 90% of the variance of the stacked participants' vmPFC voxel time series (z-scored within each participant). This requires estimating N(, ) for each component, the transition probability matrix, and the initial starting probabilities. We selected the optimal states separately for each study by finding the largest decrease in BIC with respect to k, argmin ( d _ dk (BIC ) ) .

Whole-brain univariate group-HMM state contrast
We used univariate contrasts to identify average activation in each voxel that was significantly different when participants occupied a particular state compared to all other states using the group-HMM predictions. We used a one-sample t test at the second level to identify activity changes that are consistent across participants and used FDR q < 0.05 to identify a threshold that controls for multiple comparisons. This analysis is identical to traditional analyses used in task-based fMRI, except, here, we define different conditions based on individual state occupancy. Because each participant has a unique sequence of state transitions, this analysis identifies regions at the group level that are common across individuals but vary across time, which means that these regions are based on endogenous rather than exogenous processing.

HMM state contrast Neurosynth decoding
We used meta-analytic decoding (78) to make quantitative reverse inferences of the possible psychological functions implied by the pattern of brain activation using the Neurosynth framework (122). We used topic-based maps from previous studies (79,123,124), which were generated using latent Dirichlet allocation topic modeling of 9204 fMRI articles and their corresponding coordinate data. Among the 80 topics, there were 48 related to psychological concepts, and we plot the top 10 that were most associated with each unthresholded group-HMM state contrast t map based on spatial similarity using Pearson correlations in fig. S18.

Study 3 (face expression) Participants
Twenty participants (mean [SD] age = 18.9 [0.91] years; 13 female) were recruited from the Department of Psychological Brain Sciences at the Dartmouth College for course credit.

Procedure
Participants watched the first four episodes of the first season of FNL over two separate 2-hour sessions. Here, we report results from episode one. Facial expressions during the experiment were monitored using GoPro HERO 4 cameras recording at 120 frames/s at 1920 by 1080 resolution. Each camera was positioned using a custom facecam headsets developed by our group (71). This approach is invariant to head motion and minimizes many types of facial occlusions. Recorded videos were then temporally aligned to the episodes by minimizing differences in audio intensity using our open source Python FaceSync toolbox version 0.0.8 (71). Facial behavioral features consisting of 20 facial AUs, a standard for measuring facial muscle movement based on the Facial Action Coding System (72), were extracted using FACET® (73) accessed through the iMotions biometric research platform (125). Data were downsampled to 0.5 Hz.

Face model visualization
We used our Python Facial Expression Analysis Toolbox (Py-Feat) version 0.0.1 (https://py-feat.org/) to visualize how specific features from our model correspond to changes in facial morphometry data collected during study 3 (126). Briefly, we learned a mapping between 20 facial AU intensities and 68 landmarks comprising a two-dimensional face using partial least squares implemented in scikit-learn (127) . We used 10,708 images corresponding to each frame from the extended cohn-kanade facial expression database (CK+) (128) and extracted landmarks using OpenFace (129) and AUs from iMotions FACET® engine (125). Next, we performed an affine transformation to a canonical face before fitting the model and added pitch, roll, and yaw head rotation parameters as covariates with the 20 AU features. We then fit our model using a threefold cross-validation procedure. We achieved an overall training model fit of r 2 = 0.61 and a cross-validated mean of r 2 = 0.53. We used this facial morphometry model to visualize the degree to which each AU loaded on a specific principal component. AU intensities are overlaid onto corresponding facets of the face landmark model after performing a min-max feature scaling to ensure that the values are on the original AU scale [0,4], x scaled = SD(x)(4 − 0) + 0.
Face expression loadings on the cross-experiment latent factor model can be viewed in fig. S16.

Study 4 (emotion ratings) Participants
We recruited 192 participants from the Amazon Mechanical Turk workplace to participate in a 60-min study (mean [SD] age = 37.11 [10.71] years; 105 female), during which they viewed the first episode of FNL. All participants provided informed consent in accordance with the guidelines set by the Committee for the Protection of Human Subjects at the Dartmouth College and were compensated for their participation ($9). Four participants were excluded for not having enough data to perform CF (less than 25% of samples).

Procedure
The experimental paradigm was delivered via a custom open source web application built using Flask (http://flask.pocoo.org/), jsPsych (www.jspsych.org/), psiTurk (https://psiturk.org/), and MySQL (www.mysql.com/) and served using an NGNIX (www.nginx.com/) web server hosted in our laboratory (https://github.com/cosanlab/ moth_app). For each participant, the episode was paused over the course of its 45-min runtime at random intervals of 200 to 280 s sampled from a uniform distribution (following an initial uninterrupted viewing period of 30 to 270 s). At each pause, participants were instructed to rate the intensity, if any, of 16 different dimensions: contempt, surprise, relief, anger, envy, shame, interest, elation, satisfaction, guilt, sadness, hope, pride, fear, joy, and disgust. The set of dimensions rated by each participant was presented in random order across participants. On average, participants completed 11.45 ratings (average SD = 1.93 across emotion categories). The average intertrial interval for making a rating was 229.65 s (average SD = 53.33). Ratings were downsampled to 1 Hz and used to create a subject-by-time sparse matrix (188 × 2702). A CF technique (nonnegative matrix factorization with stochastic gradient descent) was applied to resulting matrices to infer each participant's rating for every moment in time. Subjective emotion rating loadings on the cross-experiment latent factor model can be viewed in fig. S17.

Collaborative filtering
We used CF to create a time series for each affective dimension for every study 4 participant (130). CF is a machine learning technique that is commonly used by industrial recommender systems (e.g., Netflix and Amazon) to infer user preferences on many items (e.g., movies, music, and products) when their preferences are only known for a few items (131). The key assumption driving CF is that, to the extent that participants A and B have similar ratings on n samples, they will rate other items similarly. To extend this general approach to the time series affective rating data we collected in study 4, we convolved each participant's (sparse) affective ratings (i.e., on a subset of the dimensions we sought to estimate) with a 60-s boxcar function kernel and divided each time point by the number of rating overlaps so that the interpolation reflects the mean rather than the sum of the ratings. This allows us to augment our data by assuming that time points closer in time not only are more similar to each other than time points further in time but also acts as a low pass filter, which removes any fast high frequency changes that may be present in the data. Next, we used nonnegative matrix factorization with stochastic gradient descent (100 iterations) implemented in our Python emotionCF toolbox (https://github.com/cosanlab/emotionCF) to perform the matrix completion. This approach assumes that there are N "types" of participants that can be used as a basis set to linearly describe any individual participant, where N is the number of factors used in the matrix decomposition. The algorithm uses stochastic gradient descent to minimize the sum of squared error (with regularization) between the sparsely observed and predicted data. Because the dot product of the factorized matrices results in a full predicted matrix, this approach is able to make predictions for the unobserved data points for each participant. This technique allows us to reconstruct a time series of each participant's emotional ratings at every second during the show, while maintaining individual differences in rating time courses. Because we sparsely sample the subjective ratings, we believe that this rating procedure should have a minimal impact on participants' emotional experiences unlike alternative approaches that require dual monitoring to continuously report feelings on single dimensions.

SUPPLEMENTARY MATERIALS
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/ content/full/7/17/eabf7129/DC1 View/request a protocol for this paper from Bio-protocol.