Unveiling the dynamics of emotions in society through an analysis of online social network conversations

Social networks can provide insights into the emotions expressed by a society. However, the dynamic nature of emotions presents a significant challenge for policymakers, politicians, and communication professionals who seek to understand and respond to changes in emotions over time. To address this challenge, this paper investigates the frequency, duration, and transition of 24 distinct emotions over a 2-year period, analyzing more than 5 million tweets. The study shows that emotions with lower valence but higher dominance and/or arousal are more prevalent in online social networks. Emotions with higher valence and arousal tend to last longer, while dominant emotions tend to have shorter durations. Emotions occupying the conversations predominantly inhibit others with similar valence and dominance, and higher arousal. Over a month, emotions with similar valences tend to prevail in online social network conversations.

Identifying and measuring underlying emotion dimensions.As our goal is to link the components of the dynamic flow of emotions, such as carryover and transitions, to underlying appraisal dimensions, we conducted a survey to determine the dimension scores of the 24 emotions.To better represent the complex world of emotions, we identified an exhaustive set of dimensions, which includes dominance, motivational state, agency, certainty, attentional activity, effort, and time orientation as well as the frequently used dimensions of valence and arousal.Supplementary Table S3 contains the definitions of the nine appraisal dimensions in the study and Supplementary Survey details the survey conducted to determine the dimension scores of each emotion.
Analysis approach.We use a multivariate time series model based on a traditional VAR specification to investigate the temporal dynamics of emotions and how its components vary according to the underlying dimensions of emotions (see, for instance 47 for an alternative application of the general family of VAR models in the analyses of emotion dynamics).The VAR model simultaneously accommodates the following behaviors: (1) carryover in emotions, through the inclusion of the lagged values of emotions' own frequencies, (2) the transitions to all destination emotions from all other emotions, through the inclusion of lagged values of other emotions' frequencies, and (3) the co-occurrence of emotions, through a full error variance-covariance matrix.
Given our goal of describing this process over a multidimensional appraisal space, we tailor the specification of a classic VAR to fit our need.Specifically, (1) to understand which emotions are expressed more than others, we link the model parameters capturing an emotion's average expression frequency to the emotions' underlying appraisal dimension scores; (2) to shed light on how long a society is likely to express a specific emotion following a temporal boost, we relate the carryover coefficients in the model governing the duration of emotions to the emotions' underlying appraisal dimension scores; (3) to reveal the transition patterns among emotions in the short term, we express the coefficients capturing the short-term transitions from one emotion to another as a function of the distance www.nature.com/scientificreports/ between the emotion pairs in the multidimensional appraisal space.We allow the short-term transitions to be asymmetric.That is, the impact of an exogenous increase in an emotion that scores high on one dimension on an emotion that scores low on the same dimension is allowed to be different than that in the other direction, yet proportional to the distance between the emotions (e.g., the impact of a temporary boost in anger on sadness is different from that of sadness on anger).The resultant specification is parsimonious and one that produces interpretable coefficients (see "Model specification").Finally, to quantify the long-term transitions among emotions, we use post-estimation impulse-response function (IRF) analyses 48 , piecing together the carryover in, the short-term transitions among, and the cooccurrence of emotions.

Model specification.
The basic form of our VAR model is as follows: The model in Eq. ( 1) is a VARX model of order one, which we will use to illustrate how we tailor the specification.Extension to higher-order VARX models is straightforward.
E it in Eq. ( 1) is the relative frequency of emotion i (i = 1,…,24) on day t (t = 1,…,790).X 1t and X 2t are two exogenous variables included to control for the effects of the 280-characters-long tweet experiment and rollout.These step dummies take the value of 1 after September 26, 2017, and November 7, 2017, respectively.ε it are the white-noise disturbances distributed N(0,∑), where ∑ is a full variance-covariance matrix.α i , γ ij , and β i. are the parameters to be estimated.α i is the base expression level of emotion i.The vector autoregressive parameter matrix contains the carryover coefficients governing the duration of an emotional state (γ ij , for all i = j) and the coefficients capturing short-term transitions between emotional states (γ ij , for all i ≠ j).
As our goal is to describe whether and to what extent emotion dynamics are associated with the underlying dimensions, we express α i and γ ij as functions of these dimensions.Specifically, where DIM ik is emotion i's score on dimension k (k = 1,…,K).While this section presents the general model specification, exploratory factor analysis of survey data measuring the underlying dimensions reveals that a 3-dimensional space effectively distinguishes between emotions (see "Emotion dimension survey results").Thus, K = 3 in our empirical analysis.The overbar indicates that the dimension scores are mean centered across emotions.Consequently, μ 0 captures the base expression level of an emotion scoring average on all dimensions, and μ k captures how base expression level varies along dimension k.As a control, we add dictionary size (S i , the total number of unigrams and bigrams used while labeling whether emotion i is present in any given tweet).Similarly, we express the carryover coefficients as a function of the underlying dimensions and control for the effect of dictionary size.
where λ 0 captures the carryover of an emotion scoring average on all dimensions, and λ k captures how carryover varies along dimension k.Finally, we express γ ij (for all i ≠ j) capturing the short-term transitions from emotion j (i.e., the source emotion) to emotion i (i.e., the destination emotion) as a function of the distance between emotions i and j in the multidimensional appraisal space.
where The distance operationalization in Eqs.(5a) and (5b) allows for directionally asymmetric transitions in Eq. (4).That is, the specification allows the transition from a source emotion scoring low on dimension k to a destination emotion scoring high on the same dimension (i.e., moving up on dimension k) to be different than the transition in the other direction (i.e., moving down on dimension k, with a source emotion scoring higher than the destination emotion).
(1)  www.nature.com/scientificreports/ The meanings of the coefficients in Eq. ( 4) are different than those in Eq. ( 2) or Eq. ( 3).τ 0 captures the short- term effect (i.e., next-day effect) of an increase in an emotion on another emotion located exactly on the same spot in the multidimensional appraisal space but labelled differently.Such an emotion exists only theoretically.As such, τ 0 alone is not useful and has to be considered together with the other coefficients.τ + k captures how the short-term effect changes as the destination emotion moves further away from the source emotion which scores lower on dimension k (i.e., short-term transition from an emotion scoring low on dimension k to a high-scoring emotion).τ − k captures how the short-term effect changes as the destination emotion moves further away from the source emotion which scores higher on dimension k (i.e., short-term transition from an emotion scoring high on dimension k to a low-scoring emotion).Plugging in Eqs. ( 2), (3), and (4) in Eq. (1) and rearranging the terms give the final specification (see Supplementary Model), which we estimate using Feasible Generalized Least Squares.
Finally, in addition to the vector autoregressive matrix coefficient estimates, our post-estimation IRF analyses require, as inputs, exogenous shock vectors that accommodate the instantaneous effects of different emotions on the remaining ones to allow for co-occurrence of emotions.These instantaneous effects are captured in the full error variance-covariance matrix and, assuming multivariate normality, we obtain them by calculating conditional normal expectations-an idea that can be traced to 49 .Specifically, a shock of δ units to emotion i is expected to impact all other j emotions by δ × σ ij /σ ii on the same day, where σ ij is the corresponding element of the error variance-covariance matrix.

Results
Emotion dimension survey results.Using the data obtained from the survey measuring the 24 finegrained emotions over nine interrelated dimensions, we conducted an exploratory factor analysis.The analysis uncovered three higher-order factors, resembling the structure in more recent dimensional spaces 37 .The three factors that emerge closely resemble the classical valence, arousal, and dominance (VAD) framework commonly used in literature 50,51 but are broader in nature.
The first dimension is composed of valence, time orientation, motivational state, attentional activity, and effort.We label this dimension "valence" (V) for ease of exposition but acknowledge its broader meaning: An emotion scoring high (low) on valence refers to an emotional state that is positive/pleasant (negative/unpleasant), future-oriented (past-oriented), not demanding (demanding) effort but deserving (not deserving) attention, and one wherein the individuals are motivated to approach (avoid)."Arousal" (A) is a stand-alone dimension.Corresponding to its conventional definition, it distinguishes between emotions based on the level of activation: an emotion scoring high (low) on arousal indicates heightened (reduced) levels of activation.Finally, the third dimension, which we label as "dominance" (D) for ease of exposition, is composed of dominance, certainty, and agency.An emotion that scores high (or low) on dominance is one in which the person is certain (or uncertain) about how they feel and claims (or doesn't claim) responsibility and feels (or doesn't feel) independent.Supplementary Table S2 displays the emotions' scores on these three higher-order dimensions.

VAR model results.
Before estimating the proposed VAR model, whose parameters are expressed as functions of the emotions' dimension scores, we first checked for stationarity of the emotion time series using Augmented Dickey-Fuller tests and found that all our time series are stationary.Second, we determined the order of the VAR model.Comparison of model fit criteria across VAR models with different lag lengths suggested that the optimal lag length in our case is 1 (see Supplementary Table S6).Third, Granger Causality tests justified the estimation of a dynamic system capable of accounting for contemporaneous and short-term associations among emotions as well as the carryover of emotions (i.e., a VAR model) to unveil the emotion dynamics observed in OSN conversations (see Supplementary Granger Causality Test).Next, we present the results of the proposed VAR model of order one.
Frequency.First, we concentrate on the average frequency of an emotion expressed in OSN conversations (i.e., base level).We discover that the base level of an emotion's frequency decreases with valence ( µ V = − 0.000887, SE µ V = 0.000389, P µ V = 0.022), and increases with dominance ( µ D = 0.005441, SE µ D = 0.000945, P µ D < 0.001) and arousal, albeit with a marginal effect ( µ A = 0.000918, SE µ A = 0.000499, P µ A = 0.065).The emotional palette of this OSN, on average during the 790 days, is composed mainly of emotions that score lower on valence but higher on dominance and arousal.
Duration.Governed by the carryover in the time series, duration captures how long it will take an emotion to return to its normal level after being subjected to an exogenous shock.We express the durations of emotions using the P% duration interval.The interval is the number of time periods that passes before P% of the expected effect of an exogenous shock takes place and is given by ln(1 − P/100)/ln( ) − 1 , where λ is the carryover coefficient 52 .The carryover of an emotion with average valence, arousal, and dominance implies a 90% duration interval of 13.8 days ( 0 = 0.855983, SE 0 = 0.003708, P 0 < 0.001).That is, holding everything else constant, it takes approximately 13.8 days for 90% of the cumulative effect of an exogenous shock to the emotion time series to materialize.
In terms of the relationship between underlying dimensions and the duration of emotions, we find that the carryover increases with valence ( V = 0.056753, SE V = 0.002399, P V < 0.001) and arousal ( A = 0.011204, SE A = 0.001966, P A < 0.001) but decreases with dominance ( D = − 0.165068, SE D = 0.006454, P D < 0.001).The effect of an exogenous shock to a high-scoring emotion (+ 1 SD) on valence fades slower than that of a lowscoring emotion (− 1 SD)-the 90% duration intervals are 39.3 and 7.7 days, respectively.Similarly, if an emotion with a high (low) arousal score experiences an exogenous shock to its base frequency level, the conversations will be occupied by that emotion for a longer (shorter) period: for high and low arousal emotions, the 90% duration www.nature.com/scientificreports/interval is 15.4 and 12.4 days, respectively.Finally, conversations featuring emotions with higher levels of dominance die out faster (90% duration interval is 7.0 days) than those with lower levels (90% duration interval is 59.1 days).In sum, emotions with high valence and/or arousal are more likely to occupy the OSN conversation for longer, whereas emotions with high dominance are less likely to do so.
Short-term transition.The short-term transitions are myopic cross-effects governed by cross-lagged associations among the emotion time series (i.e., the change in the frequency level of an emotion on the day after another emotion experiences a change).We find that, when the frequency of an emotion increases on a given day, the frequencies of other emotions positioned extremely close to the source emotion (i.e., to the point that distance becomes negligible) decrease on the following day ( τ 0 = − 0.011279, SE τ 0 = 0.000929, P τ 0 < 0.001).
The magnitude of suppression decreases as the valence distance between the source emotion (i.e., the emotion that experiences the boost) and the destination emotion (i.e., the emotion whose next-day frequency is going to be impacted) increases both in the upward direction ( τ + V = 0.001480, SE τ + V = 0.000342, P τ + V < 0.001) and in the downward direction (τ − V = 0.001589, SE τ − V = 0.000323, P τ − V < 0.001).Valence-distance effect turns out to be symmetric: the source emotion impacts equidistant destination emotions above and below itself identically (χ 2 (1) = 0.04, P = 0.841).The same pattern is observed for dominance: the source emotion suppresses distant destination emotions on the dominance dimension less ( τ + D = 0.003724, SE τ + D = 0.000730, P τ + D < 0.001 and τ − D = 0.0036949, SE τ − D = 0.000684, P τ − D < 0.001) and in similar magnitudes (χ 2 (1) ≈ 0, P = 0.983).In sum, a boost in a source emotion draws disproportionately more (less) from the neighboring (remote) emotions on the following day than it does from the remote (neighboring) emotions over the valence and dominance continua.
Short-term transitions are influenced differently and asymmetrically by the relative positions of source and destination emotions on the arousal dimension.Following an increase in a source emotion's frequency, destination emotions with higher levels of arousal are suppressed and increasingly more based on their arousal distance ( τ + A = − 0.001478, SE τ + A = 0.000422, P τ + A < 0.001).Destination emotions with lower levels of arousal are suppressed as well, but equally, as the arousal distance effect in this direction is insignificant ( In sum, a boost in a source emotion draws disproportionately more from higher arousal emotions on the following day, and equally, from all lower arousal emotions. The short-term suppression of all destination emotions in response to a boost in a source emotion coupled with the significant carryover of the boost in the source emotion may suggest at the first glance that the surface area of this emotional palette is constrained (i.e., the temporary rise in one emotion comes at the expense of others).However, the finding that the amount of suppression in destination emotions is non-uniform and varies along the three dimensions, and that the pattern of variation observed along the valence and dominance dimensions is different from that of the arousal dimension, suggest other mechanisms might be at play.
One such mechanism that comes to mind is the imitation in the emotion contagion literature 53 , which may explain especially the pattern of results observed over the valence and dominance continua.If imitation-driven contagion holds, members of the OSN experiencing emotion-eliciting events that could be appraised similarlybut not identically-as the emotion which recently occupied the conversations can label their experiences with that specific emotion, rather than what actually fits (e.g., expressing happiness due to its recent takeover of OSN conversations, even if joy or amusement would have been more appropriate with the actual emotion-eliciting events).The pattern of results observed over the arousal continuum, on the other hand, seems to be guided by a different mechanism, one of emotion regulation.Emotion regulation strategies, such as suppression and reappraisal, can inform how close or far the most impacted destination emotion will be to the source emotion 54 .Our findings suggest a tendency to down-regulate the arousal level of these aggregate-level emotions, probably due to higher-arousal emotions-emotional states of excitement, activation, and stimulation-being more difficult to maintain than their counterparts.If such mechanisms are at play, then they would be visible in associations among emotions at other isolated time slices; for instance, the same day as the source emotion experiences the boost.
Co-occurrence.To test this idea, we turn to IRF analysis and examine how the contemporaneous effects of 10% exogenous shocks to different source emotions on destination emotions (i.e., IRFs on day 0) vary as a function of asymmetric distances between emotion pairs.The regression results (Table S8, panel labeled CE Regression) show that, consistent with a contagion prediction, emotions that are close in valence tend to co-occur more than those that are far apart ( CE C = 0.021172, SE CE C = 0.003541, P CE C < 0.001; A > 0.100).However, the directions of the coefficient estimates suggest that lower-arousal (higher-arousal) emotions may co-occur more (less) with the source emotion that experiences the boost, consistent with the tendency to down-regulate on arousal.
These conceptually consistent yet directionally opposite findings obviate the need to assess the combined effect of emotion co-occurrence and short-term transitions among them, and to bring in the carryover in emotions to complete the picture.The long-term transition results discussed below combine the contemporaneous association in emotion frequencies due to co-occurrence with the carryover in emotions and the myopic crosseffects among them.www.nature.com/scientificreports/Long-term transition.To investigate the long-term transition among emotions, we trace the impact of a 10% exogenous shock, applied one at a time, to each and every source emotion on all other emotions over a 30-day period, including the day of the shock (day 0).Long-term transition is operationalized as the cumulative IRF (CIRF) between days 1 and 29.The CIRF represents the total incremental change in the frequency of an emotion and indicates how much more-or less-the emotion is expected to occupy OSN conversations in the long run.First, we show how an unexpected increase in each emotion affects how much other emotions are expressed in the long run in two ways.Using heatmaps, Fig. 2 depicts the transition likelihood of emotions across three dimensions.According to the observed pattern, emotions that are closer in valence have a higher likelihood of long-term transition, as indicated by a higher number of warmer colors that are closer to the diagonal.In Fig. 3, we show the incremental changes in all destination emotions after an exogenous shock to two exemplary source emotions, happiness, and anger, across the VAD space.The figure, for example, suggests that amusement, which is close to happiness in terms of each dimension, increases the most.
Second, we regressed the CIRFs on the asymmetric distance between emotion pairs to investigate the relationship between emotion dimensions and long-term transitions (Supplementary Table S8, panel labeled CIRF Regression).We find that (1) long-term transitions to destination emotions close to the source emotion on valence dimension are greater than those to distant destination emotions ( CIRF C = 0.012999, SE CIRF C = 0.003799, P CIRF C < 0. > 0.100) between emotion pairs.These findings imply that the carried-over contemporaneous effect (i.e., co-occurrence) overwhelms short-term suppression and that duration differences are not

Discussion
Summary.Analyzing millions of social media posts retrieved from Twitter and processed with NLP techniques, this study investigated (a) how much specific emotions occupy OSN conversations, (b) how long they last, and (c) how they follow each other in short-and long-term timeframes and expressed these quantities of interest as a function of three higher-order appraisal dimensions (i.e., valence, arousal, and dominance).We discovered that emotions with lower valence but higher dominance and/or arousal are more likely to occupy OSN conversations; and that the duration of an emotion's occupation of OSN conversations increases with valence and arousal but decreases with dominance.When an emotion takes over OSN conversations, it suppresses others with similar valence and dominance and higher arousal notably in the short term.In the long run, emotions with similar valences are more likely to follow-up and occupy OSN conversations.

Contributions.
To the best of our knowledge, this study is the first to explore the dynamics of a very large and fine-grained set of emotions and describe these dynamics over an exhaustive set of underlying dimensions.Uncovering the dynamic flow of emotions in OSNs may have important implications for political, economic, and societal outcomes.The role of emotions has been explored in various domains, such as news consumption 55 , false stories 56 , and political content 11 , demonstrating which emotional content spreads more or quickly.Our findings on the evolution of emotions over time can be leveraged to create communication interventions for responding to rising emotional trends effectively.For instance, in times of public health emergencies 57 or cascading collective traumas 58 , people may experience and express heightened anxiety along with other emotions on social media.Policymakers can benefit from an understanding of the duration of these emotional responses, as well as the potential for subsequent emotions, and finetune their communication strategies.Such informed interventions can help mitigate the negative impacts that exposure to specific emotions through social media can have on public welfare.
Our findings also contribute to the literature by highlighting the role of an overlooked dimension that distinguishes between emotions: dominance.Composed of certainty, agency, and dominance, this higher-order dimension appears as a key descriptor of the dynamic flow of emotions.As evidenced by the differences between www.nature.com/scientificreports/low-vs.high-scoring emotions' 90%-duration intervals, its greatest impact is felt on how long emotions linger in OSN conversations.Dominance is also associated with which other emotions arise as the dynamic flow unfolds.Consider pride, hope, and awe, three emotions that score similarly on valence and arousal but quite different from one another on dominance.Our findings suggest that OSN conversations featuring pride, the emotion with the highest dominance score among the twenty-discrete emotions in this study, will die out much faster than the other two.Assuming away the minor differences in valence and arousal scores of these three emotions, our findings also indicate that awe will be more prevalent in OSN conversations than hope as pride's grip starts to loosen.Whereas one may postulate why and how the underlying dimensions of valence and arousal are associated with the components of the dynamic flow of emotions in the way they are, our current understanding of dominance prevents us from developing that logic.We believe this represents a fruitful avenue for future research.

Limitations and avenues for future research
Although the broad range of cognitive appraisal dimensions considered in this study allowed us to identify the novel association between dominance and the dynamic flow of emotions, the list is by no means complete.Consider individuals regulating self-focused emotions (e.g., sadness) or self-conscious emotions (e.g., shame).The potential differences in their use of OSNs-narrowcasting (i.e., communicating with only one person) rather than broadcasting (i.e., communicating with many people) their emotional experiences 59 -implies that the frequency with which certain emotions are expressed in OSN conversations, how long they appear to last, and where they may transition may vary along dimensions other than the three dimensions we investigated.Therefore, future research could explore how other emotion categorizations describe their dynamic flow in OSN conversations.While this study advances our knowledge of the evolution of emotions in social networks, it is important to note that it does not explore the role of social network structures and user characteristics on the results or distinguish the individual vs. collective nature of emotions and disentangle the mechanisms that give rise to them.The structure of networks can influence the diffusion of behaviors and mental states, such as depression 60 , obesity 61 , exercising 62 , and high-risk movements 63 .Future research could examine how social network structures impact the persistence and transformation of emotions such as pride, gratitude, and contentment, which are known to benefit from social support 64 .In addition to network structures, social network members play a critical role in the spread of behaviors or products.Gender and age have been found to be significant factors in susceptibility and influence within social networks 65 .Demographics may also impact the expression and evolution of emotions online, with men tending to display more assertiveness or dominance-related emotions and women showing more nurturing or empathy-related emotions 66 .Additionally, the presence of strong ties and intergroup conflicts in social networks may serve as predictors of emotional evolution.Research has shown that strong ties are instrumental in spreading both online and real-world behavior in human social networks 67 , while the outgroup effect has been found to be a stronger predictor of social media sharing than emotional language 68 .Taken together, these findings suggest that emotions related to outgroups may lead to greater conflict and prolonged durations, whereas emotions related to ingroup identity may promote emotional convergence and shorter durations within the group.
Moreover, this study describes the dynamics of an aggregation of individually expressed emotions.These individuals are members of a society with a history of common experiences and collective memories, socially shared cognitive appraisal structures, and similar evaluative attitudes, appraising the emotion eliciting events of their everyday lives in relation to their overlapping private concerns or socially grounded shared concerns 69,70 .As such, this study depicts the dynamics of moderately collective (i.e., weak we-mode) emotions 69 at best.However, there are situations where collective emotions may be more prevalent, such as appraising a singular emotion eliciting event relevant to a preexisting group of individuals with sense of collective commitment [71][72][73] .Future research should investigate whether and how the dynamics of strongly collective emotions in social networks (i.e., strong we-mode emotions) differ from those identified in this study.
In this study, we investigate the dynamic flow of emotions using daily time-series data obtained by aggregating over emotions extracted using dictionary-based methods from posts on the microblogging site Twitter originated from Turkey-based IP addresses.Future research should pay attention to the various challenges posed by these choices.First, there are alternative approaches to extracting emotions from online text: bottom-up (i.e., machine learning methods) and top-down approaches (i.e., dictionary-based methods).Although there is no single best method that predicts sentiments well, as demonstrated in the context of consumer mindset metrics 74 , bottomup methods require large training data that is already classified 75 and perform better in domains in which they are developed 76 .Dictionaries, on the other hand, are transparent and easier to apply.As the constructs (i.e., discrete emotions) were clearly defined and their operationalizations were known, we opted for a top-down approach in this study following 77 .The lack of off-the-self dictionaries for the twenty-four emotions prompted us to develop them from scratch.Creating non-English dictionaries contributes to the establishment of global scientific work in emotion extraction directly and indirectly via the possibility of using their output as features in ensemble machine learning applications to improve predictions [78][79][80][81] .Yet, future research might investigate various analysis techniques and compare which ones are more effective and efficient in the extraction of a finegrained set of emotions.Moreover, we investigate the durations of and transitions among emotions using daily time-series.Performing similar analysis on more finely sliced time-series data (e.g., hour or minute scale) may uncover a richer set of insights.
Second, this study exemplifies the power of emotion-tracking on platforms like Twitter that offers immense potential for understanding large-scale societal trends.Yet, building upon this approach, one must be conscious of the ethical implications and concerns associated with monitoring emotions at a large-scale on a platform such as Twitter.This study presents the emotional dynamics within a society at an aggregate level and does not intend to identify or target specific individuals' or groups of individuals' emotional changes over time.Thus,

Figure 2 .
Figure 2. CIRFs capturing long-term transitions.Emotions are positioned in ascending order from bottomleft corner for each dimension: valence (A), arousal (B), and dominance (C).Each cell in the matrix represents how much more (or less) an emotion on the corresponding row will occupy the OSN conversations when the emotion in the corresponding column experiences an exogenous shock.Warm (cold) colors indicate that the emotion on the corresponding row will occupy the conversations more (less).The heatmap was created using heatmap package in MATLAB R2020a version (https:// www.mathw orks.com/ help/ matlab/ ref/ heatm ap.html).

Figure 3 .
Figure 3.Long-term transitions to all destination emotions in response to a 10% exogenous shock to happiness (top row) and anger (bottom row).Emotions are positioned in the two-dimensional spaces by pairing valence, arousal, and dominance.The bubbles are proportional to the magnitude of the effect, with blue (red) colors indicating an increase (a decrease) in OSN conversations.The yellow (green) star marks the location of the source emotion happiness (anger).