Global patterns of synchronization in human communications

rsif.royalsocietypublishing.org Global patterns of synchronization in human communications Alfredo J. Morales1,2, Vaibhav Vavilala1, Rosa M. Benito2 and Yaneer Bar-Yam1 1 Research New England Complex Systems Institute (NECSI), 277 Broadway Street, Cambridge, MA 02139, USA Grupo de Sistemas Complejos, Universidad Politécnica de Madrid, ETSI Agronómica, Alimentaria y de Biosistemas, Avenida Computlense S/N, 28040 Madrid, Spain 2 AJM, 0000-0002-8509-0839 Cite this article: Morales AJ, Vavilala V, Benito RM, Bar-Yam Y. 2017 Global patterns of synchronization in human communications. J. R. Soc. Interface 14: 20161048. http://dx.doi.org/10.1098/rsif.2016.1048 Received: 23 December 2016 Accepted: 8 February 2017 Social media are transforming global communication and coordination and provide unprecedented opportunities for studying socio-technical domains. Here we study global dynamical patterns of communication on Twitter across many scales. Underlying the observed patterns is both the diurnal rotation of the Earth, day and night, and the synchrony required for contingency of actions between individuals. We find that urban areas show a cyclic contraction and expansion that resembles heartbeats linked to social rather than natural cycles. Different urban areas have characteristic signatures of daily collective activities. We show that the differences detected are consistent with a new emergent global synchrony that couples behaviour in distant regions across the world. Although local synchrony is the major force that shapes the collective behaviour in cities, a larger-scale synchronization is beginning to occur. Subject Category: Life Sciences – Physics interface Subject Areas: biocomplexity Keywords: complex systems, computational social science, synchronization, human behaviour Author for correspondence: Alfredo J. Morales e-mail: [email protected] Electronic supplementary material is available online at https://dx.doi.org/10.6084/m9.figshare.c.3694468. 1. Introduction The functioning of complex systems, like human societies or living organisms, depends not only upon the individual functionalities of their parts but also upon the coordination of their actions. Self-sustaining activities, such as economic transactions and associated communications, occur through interactions among people, creating dependencies among their actions. A central challenge for both sociology and economics is our ability to characterize the collective actions of individuals that together become the aggregate activity that constitutes our society [1]. Recent studies have shown that these processes can be observed by looking at communication patterns among individuals in social groups [2]. Here we analyse Twitter data to describe the underlying dynamics of social systems. In particular, we study collective activities across geographical scales, from areas smaller than 1 km2 up to the global scale. The recent explosion of social media is radically changing the way information is shared among people and therefore the properties of our society. These new mechanisms allow people to easily interact with each other and to affordably exchange and propagate pieces of information at multiple scales. As a consequence, people may be able to engage in types of complex tasks previously dominated by organizations structured for a particular purpose [3]. By looking for patterns in the aggregate data, we can retrieve structural and dynamical information about the social system [4]. This represents an unprecedented opportunity to study social systems across many scales. Traditional surveys of small samples, which are typically limited to a few questions, do not have the scale and frequency to capture such population dynamics [4]. As highly concentrated social systems, cities are manifestly complex systems with emergent properties [5]. They are self-organized entities made up of multiple complex agents that engage in larger-scale, complex tasks. Moreover, cities have multiscale structures individually through fractal growth and collectively through size distributions. Their structural patterns have been modelled by scaling laws [1], archetypes of streets layouts [6,7] and land use [8]. Humangenerated data have been used to understand the dynamical behaviour of & 2017 The Author(s) Published by the Royal Society. All rights reserved. 2 rsif.royalsocietypublishing.org inhabitants and their impact on the functioning of a city. Patterns of human activity and mobility reveal the spatial structure of collective interactions [9,10] and the dynamical properties of urban functional areas [11,12]. Many of these studies use mobile phone data, which are available only for a small set of cities. In this work, we analyse over 500 million geolocated tweets, posted between 1 August 2013 and 30 April 2014, to explore patterns of social dynamics in urban areas around the world. We collected these data using the Twitter streaming application programming interface (API) [13], which provides over 90% of the publicly available geolocated tweets [14] in real time. Twitter is an online social network whose users share ‘micro-blog’ posts from smartphones and other personal computers. Its population trends younger, wealthier and urban [15,16], which makes it a good probe of the dynamics of young workers in cities. Geolocated tweets provide a precise location of the individuals that post messages, and represent around 3% of the overall Twitter stream [17]. Twitter activity has been analysed to understand human sentiments [18], news sharing networks [19] and influence dynamics [20], as well as global patterns of human mobility [21], activity [22] and languages [23]. 2. Urban activity In figure 1, we show the hourly number of tweets during an average week for a few major metropolitan areas (rectangular insets) on top of a map representing the global density of tweets during an average day (52 metropolitan areas across the world are in the electronic supplementary material). To construct the average week, we count the number of tweets in each hour in the urban area i during the observation period (N weeks), si,t. Time can be written in terms of the hour of the week t ¼ t0 mod W, where t e f1, . . .,Wg, W ¼ 168, is the number of hours per week and t0 is the number of hours since the start of the observation period. We then average the corresponding hours of each week (with the same value of t) after normalizing by the standard deviation for that day: 0 1 P XB s si,tþWðw1Þ  ð1=DÞ 23 1 N1 i, s þDbt=DcþWðw1Þ C s¼0 si,t ¼ @ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A, P P23 N w¼0 2 ð1=DÞ 23 ðs s  ð1=DÞ Þ s¼0 i,sþDbt=DcþWðw1Þ s¼0 i,sþDbt=DcþWðw1Þ where we use a 24 h daily index s e f0, . . . , D 21g, D ¼ 24, to define the daily average and standard deviation. bxc is the integer part of x. We further define an average day as the average over corresponding hours of the days of the average week: ^si,s ¼ 1 X 1 V si,sþDd , V d¼0 where s [ f0, . . . , D 21g and V ¼ 7. ð2:2Þ ð2:1Þ Overall, cities present similar patterns of collective behaviour, cycling between peaks and valleys of activity. Such patterns are also found in phone calls [24], electricity consumption [25] and emails [26]. Peaks occur during daytime or evening, indicating that people are awake and active, simultaneously tweeting from work, recreational or residential areas, whereas valleys occur during night and sleeping hours, indicating that people are inactive. The time series’ regular behaviour indicates that people synchronize their activities throughout the day. This synchrony J. R. Soc. Interface 14: 20161048 Figure 1. Global Twitter activity. Background map: Twitter activity in each 0.258  0.258 geographical area (base-10 log scale at lower right). Rectangular insets: Average week of Twitter activity of selected cities in Universal Time (UTC) after subtracting the mean and normalizing by the standard deviation. Square insets: low (blue) and high (red) points of Twitter activity of several urban areas compared with daily sunlight periods (yellow) during the nine-month observation period (scales on lower left shown for Santiago are the same for all cities). An animated visualization of the global Twitter activity is shown in the electronic supplementary material, video S1. (a) (b) 3 rsif.royalsocietypublishing.org ECG 0.08 0.07 0.06 0.05 p 0.04 0.03 activity 0.01 0 –2 M T Th W F S 0 –6 Su –4 –2 0 z-score 2 4 6 Figure 2. Correlation of the temporal dynamics of cities and heart beats. (a) An example of heart beat ECG signal at approximately 80 beats per minute (red) and the average week of Twitter activity for three cities: São Paulo (yellow), Jakarta (blue) and London (green). Vertical black lines show the time of synchronization (see text). (b) Correlation of the heartbeat with 50 000 random series (grey curve), other heartbeats (red line), periodic signals (magenta lines, from left to right: sawtooth, squared and sinusoid), and all urban areas coloured by group determined by clustering analysis (see §3 and the electronic supplementary material). ÁA(q)Á 1.50 Tokyo Jakarta Bangkok Moscow Paris London São Paulo New York Los Angeles 0.75 6 0. 8 1. 0 1. 2 0. 2 4 0. 0. 0 0 q (10–4 Hz) activity Figure 3. Spectral analysis of Twitter activity (amplitude of the Fourier transform) of major urban areas (more cities in the electronic supplementary material). The dashed lines indicate (from left to right) the frequencies (q) corresponding to the periods of 24, 12 and 8 h respectively. Tokyo Jakarta Bangkok Moscow Paris London São Paulo New York Los Angeles 2 0 –2 M T W Th F S Su Figure 4. Modelling the Twitter activity of major urban areas by spectral decomposition (more cities in the electronic supplementary material). Hourly number of tweets during an average week (blue dots) are compared with model results from equation (2.3) (red curves). J. R. Soc. Interface 14: 20161048 0.02 2 4 Ne Sã Ba M w Ist To Lo oP J ak ng os Yo an ky nd au ko art c b r o o o k lo ul k o a w n les M ge An Lo s 0h 1h 2h 3h 4h 5h 6h 7h 8h 9 h 10 h 11 h 12 h 13 h 14 h 15 h 16 h 17 h 18 h 19 h 20 h 21 h 22 h 23 h Figure 5. Spatio-temporal dynamics of Twitter activity in urban areas. Each row shows activity during an average day according to UTC time for the specified city. Colours indicate the normalized excess of activity from the average value at that location (scale shown in figure). Animated visualizations of Twitter activity in urban areas are shown in the electronic supplementary material, videos S2– S4. Tokyo Jakarta Bangkok Moscow Mexico New York max min Istanbul London 0.12 PDF 0.10 0.08 0.06 0.04 0.02 0 0 10 20 30 distance from centre (km) Figure 6. Distribution of tweets as a function of the distance to the city centre (calculated as the centre of gravity of the spatial activity of each city) during the most contracted (blue) and expanded (red) periods between 09.00 and 00.00 h in major urban areas. PDF, probability density function. is not solely due to external factors like light and dark or due to biological factors like circadian rhythms [27]. The second set of insets show low (blue) and high (red) points of the activity along with the time of sunrise and sunset over the year (yellow shadowed area). The wide range of light and dark times does not cause a comparable shift in activity times. We calculated the time difference between the series’ morning valleys and sunrise times, as well as the time difference between the series’ afternoon peaks and sunset times. We grouped these time differences into 10 day intervals, calculated their distributions and compared with a null hypothesis that the distributions do not change. We found that the average largest and shortest time differences over the observation period are significantly different ( p , 0.01 for equatorial cities and p , 0.001 otherwise), indicating that variations in the sunset or sunrise times do not determine the times of peaks or valleys of activity. Our economic system is based upon transactions, communications and coordination involving the activities of multiple workers. The completion of tasks within a given time frame depends upon the joint availability of workers either simultaneously or in the correct sequence [28]. Synchrony has its costs, as commuting traffic jams illustrate, but many activities are less effective or impossible to do J. R. Soc. Interface 14: 20161048 ex ic rsif.royalsocietypublishing.org 0 0.2 0.4 0.6 0.8 5 Bangkok Moscow Paris London New York Mexico 10 15 hour of the day 5 20 Figure 7. Radius of gyration (rg) of tweets during an average day in major metropolitan areas. Series are shown in local time and have been rescaled by subtracting the average and normalizing by the standard deviation. Blue shading indicates standard work hours (09.00 to 17.00 h) and grey shading indicates standard recreation and rest hours before midnight. Colours indicate the results of the clustering algorithm (see §3). Table 1. Maximum and minimum radius of gyration (rg) of tweets during an average day for eight major metropolitan areas in kilometres. The difference of their magnitudes is significant ( p,0.001). Other cities are in the electronic supplementary material, C. city max. rg min. rg city max. rg min. rg Tokyo Bangkok 23.855 + 0.552 15.047 + 0.382 21.413 + 0.612 13.251 + 0.401 Jakarta Moscow 13.671 + 0.265 11.157 + 0.183 12.826 + 0.270 9.516 + 0.219 Paris New York City 4.066 + 0.053 38.150 + 1.119 3.690 + 0.061 35.572 + 1.158 London Mexico 13.545 + 0.255 12.977 + 0.368 11.892 + 0.320 11.135 + 0.359 without it. Synchrony enables couples in relationships to share waking and sleeping schedules. Broad categories of coordinated behaviours like work, leisure and sleep make up the temporal superstructure which organizes all other tasks within the daily time line of a city. For workers on a 09.00 to 17.00 h schedule, working at the same time every day enables them to meet to conduct business activities together, whether in person or by telephone. Others who work outside of regular business hours are able to provide services like entertainment and shopping opportunities to those who work during the primary shift. The coordination of social activities during these off hours is possible because of the synchrony of standard work and rest hours. Biological circadian rhythms are important for the synchronization of sleeping hours [27] and the interactions of couples contribute to the synchronization of activities. Similar patterns arise in the biological activity of living organisms, like heartbeats or respiration, or in their collective activity, like in termite colonies [29] or ecosystems like forests [30]. Heartbeats, in particular, have properties that appear in some ways similar to urban dynamics. For comparison, we show in figure 2a the electrocardiogram (ECG) of a 43-year-old man [31,32] together with the Twitter activity from São Paulo (yellow), Jakarta (blue) and London (green). The similarity between heartbeats and Twitter activity is remarkable and quantified in figure 2b by correlating ECG signals of individual heartbeats with urban Twitter activity (also see the electronic supplementary material, B). The signature of a regular heartbeat is obtained by segmenting the ECG into equal average heartbeat intervals that are further divided into 24 segments (similar to the 24 h in a day). This signature is correlated with the ECG and Twitter activity. The correlation is done by placing the minimum value in each period for both signals at the centre of the correlation window. The heartbeats are highly correlated with the Twitter activity in urban areas, just less than the correlation of heartbeats with each other. The correlations with the time series are compared with those of 50 000 random time series, as well as with those of periodic series, in figure 2b. While the high level of correspondence is not essential to our discussion, the reasons for it can be understood. Both regular heart activity and human urban activity have three primary periods. The heart experiences a strong (ventricular) contraction, a secondary (atrial) contraction and a period in which both are relaxing. Human urban collective activity has a primary work shift, a secondary work and recreation shift, and a sleep shift. The threefold cyclical Twitter behaviour was further analysed by spectral decomposition (Fourier transform). The spectral behaviour of the Twitter activity series from six major cities is shown in figure 3 and the remaining cities are shown in the electronic supplementary material. All frequency J. R. Soc. Interface 14: 20161048 0 Jakarta rsif.royalsocietypublishing.org 3.0 rg 1.5 0 –1.5 –3.0 Tokyo (b) (c) 0.9 0.8 0.7 0.6 0.5 0.5 0 0 5 10 15 hour of the day 20 0 5 10 15 hour of the day 0.6 0.7 0.8 0.9 1.0 Gini coeff. work clusters 0.2 20 0.4 0.6 0.8 Twitter activity 1.0 Figure 8. Clusters of frequently visited locations according to the time of the day of individual activity. Dominant location clusters have primary activity during either conventional work (09.00 to 17.00 h) or rest hours according to local time. (a) Total activity in all cities at clusters whose primary activity is during conventional work hours. (b) As in (a) but for clusters whose primary activity is not during work hours (scale is shown in the figure). (c) Geographical heterogeneity (similar to Gini) coefficient of conventional work and rest hours locations. where t is time in hourly resolution, u represents the respective signal phase and a is the signal amplitude in the range [0, 1]. We fit the parameters u and a for each time series by minimizing the quadratic error. The model fits well the observed data ( p , 0.001), as shown in figure 4; electronic supplementary material, F. 3. Spatial patterns While there are social behaviours that differ among individuals and cultures, there are also those that are common and universal such as the very existence of cities and urban areas. In cities, many people concentrate in a few but dense business or commercial areas during work hours, whereas they disperse to typically sparse residential areas at rest hours. We expose this behaviour by looking at both spatial variation of Twitter activity and individual mobility patterns. We first disaggregated the average day of Twitter activity into a lattice of 20  20 patches in each urban area. In figure 5, we show patches of local activity for 10 major metropolitan areas after subtracting the average, normalizing by the standard deviation and colouring the activity above average values (see equation (2.2) where i represents each 3 2 1 coordinate-2 spectra have three significant components at 24, 12 and 8 h (dashed lines). The first is due to variations associated with the daily cycle, the second to variations during 12 h periods, night and day, the third corresponds to periodic variations within work, recreation and sleep ‘shifts’. Based on the frequency decomposition, we can model the kinetics by adding three sinusoid signals of 24, 12 and 8 h periods, respectively. In the model, the activity s(t) is defined as:     2pt 2pt sðtÞ ¼ a24 sin þ u24 þ a12 sin þ u12 24 12   2pt þ u8 , þ a8 sin ð2:3Þ 8 0 –1 –2 –3 –4 –3 –2 –1 0 1 coordinate-1 2 3 4 Figure 9. Multidimensional scaling and clustering of city activity according to their time series vectors in local time. Colours indicate the results of the clustering algorithm (see text). Star symbols represent Asian and Oceanian cities. Circular symbols represent Middle Eastern, European and African cities. Triangular symbols represent South and North American cities. Axes correspond to reduced dimensions obtained from multidimensional scaling. patch). The average and standard deviation are for each patch, rather than the whole city (see electronic supplementary material, C). In all cities, there are peaks of intense activity occurring near central areas which expand towards more peripheral areas over time. In figure 6, we show the distribution of tweets as a function of the distance to the city centre, during the most contracted (blue) and expanded (red) times J. R. Soc. Interface 14: 20161048 frequently visited locations 6 1.0 rsif.royalsocietypublishing.org Gini coeff. home clusters (a) Jakarta Manila Tokyo Sydney Pacific O. Mumbai London Berlin Istanbul Riyadh Atlantic O. Mexico Chicago New York Buenos Aires Rio de Janeiro Los Angeles Pacific O. Hawaii Pacific O. M 1.0 0.9 T 0.8 0.7 0.6 Th time 0.5 F 0.4 0.3 S 0.2 Su 0.1 –180 –150 –120 –90 –60 –30 0 30 longitude (b) 60 90 120 150 180 0 (c) Figure 10. (a) Temporal dynamics of an average week of Twitter activity by longitude. The vertical axis represents time (increasing from top to bottom) and the horizontal axis represents longitude. Significant cities are indicated at the top. Diagonal dashed lines show peaks of activity (black) and inactivity (white) tracking the time of day. Horizontal line (solid black) indicates synchronous linked activity across Europe, Asia, Africa and Oceania (scale on right). (b) Urban correlation network across a time window from 15.00 to 03.00 UTC. (c) As in (b) but across a time window from 01.00 to 13.00 UTC. Colours indicate the results of a clustering algorithm [38], after aggregating the networks over time. An animated visualization of the urban correlation network is shown in the electronic supplementary material, video S5. between 09.00 and 00.00 h. The city centre is calculated as the centre of gravity of the spatial activity. For each city, we compared these two distributions, with a null hypothesis that they are similar to each other. After applying bootstrapping, we found that the average distance of tweets to the city centre differs significantly during the most contracted and expanded times ( p , 0.001). This effect is also manifest in the hourly variation of the radius of gyration (rg) in figure 7. We calculate the hourly radius of gyration by performing bootstrapping at each hour of the day across the whole observation period and averaging across the same hour of all days. The radius of gyration of each city shows a daily cycle of contraction and expansion during work (blue shaded region in figure 7) and rest hours (grey shadowed regions in figure 7), respectively. Table 1 shows the maximum and minimum values of the radius of gyration between 09.00 and 00.00 h. In all urban areas, the radius of gyration varies significantly ( p , 0.001). We apply bootstrapping in the following way. For each hour of the day h, we take N ¼ 500 sample sets fh,i of M ¼ 500 tweets j and calculate the tweets’ distance to the city centre dj. Then we calculate the average distance P mfh;i ¼ 1=M j[fh,i dj for each sample set, as well as the average P distance across all sample sets m ^ h ¼ 1=N i mfh;i , standard qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P deviation s ^ h ¼ 1=N i ð^ mh  mfh,i Þ2 and standard error pffiffiffiffiffi ^ h = M. We determine hmax and hmin as the times where s h ¼ s ^ h is either the maximum or minimum between 09.00 and m 00.00 h. We determine the p-value that m ^ hmax and m ^ hmin are part of the same distribution. As m ^ hmax and m ^ hmin are selected from 24 values for extremality, we used extreme value theory [33]. Using Monte Carlo sampling, the p-value that m ^ hmax is within the m ^ hmin distribution and vice versa is p , 0.001 in all cases shown and in over 90% of the cities included in the electronic supplementary material. Analogous procedures are performed with the radius of gyration obtaining similar results. J. R. Soc. Interface 14: 20161048 W rsif.royalsocietypublishing.org (a) 7 In figure 10a, we show patterns of collective behaviour at a global scale after aggregating tweets by longitude. Each longitude has cycles of activity similar to those of individual cities (figures 1, 2 and 5). Minima (white dashed line) and maxima (black dashed line) shift from east to west due to diurnal synchronization of sleep and wake cycles and the Earth’s rotation. The ubiquity of this pattern manifests 8 2.0 Z-score 1.5 1.0 0.5 0 –0.5 –1.0 –1.5 J. R. Soc. Interface 14: 20161048 4. Global synchrony (a) 2.5 rsif.royalsocietypublishing.org (b) 2.5 2.0 1.5 Z-score Second, we analysed the most frequently visited locations of each user. By applying a clustering algorithm [34], two clusters of frequently visited locations were identified (figure 8). In one cluster, most tweets are sent during work hours (after 09.00 and before 17.00), while in the other cluster most tweets are sent during rest hours (after 20.00 and before 02.00). This technique has been used to identify work and home locations from mobile phone data [35]. In general, work locations are less homogeneously distributed than residential locations. We counted the number of work and residential locations in each patch of the 20  20 grids, respectively. We found that work locations are more spatially clustered, which results in a higher spatial heterogeneity (similar to Gini) coefficient (figure 8c). Moreover, the average distance between residential locations with respect to the city centre is significantly larger than that of work locations ( p , 0.001 for half of the analysed cities), indicating that home locations are more widespread. Despite overall similarities, cities have distinct signatures in the number and shape of peaks of activity in both time (figures 1 and 2) and space (figure 5). By applying a clustering algorithm [34] to the time-series vectors, starting from the minimum of activity, we found an optimal partition [36] of three clusters of cities with remarkable cultural and regional affinity. These clusters have been coloured accordingly in figures 1 and 2, as well as in the dimensionally reduced space [37] shown in figure 9. One class of cities, including Jakarta and other Asian and Oceanian cities (blue series in figure 1 and blue symbols in figure 9), has a single large peak of activity during the day. Another class, including São Paulo and multiple North and South American cities (yellow series in figure 1 and yellow symbols in figure 9), has two small peaks of activity in the morning and a large peak in the evening. Finally, a third class, including London and multiple Middle Eastern, European and African cities (green series in figure 1 and green symbols in figure 9), has two equally sized peaks of activity, respectively, at morning and afternoon. Differences are also manifest spatially (figure 5). Asian cities (top three rows) gradually increase their activity (coloured patches), showing spatial peaks, and then rapidly decrease it (black patches). European cities (middle three rows) have a strong spatial peak of activity in the morning near the centre of the city and other dispersed peaks in the afternoon at peripheral areas. Finally, North and South American cities (bottom four rows) have several smaller peaks of activity around multiple centres and one large peak at the end of the day throughout the city. Interestingly, the morning peaks of the European cities coincide in time with the large afternoon peaks of Asian cities (see columns 8 h–10 h), which is an indication of synchrony. This synchrony is manifested as simultaneous peaks of activity in the time series (vertical black lines in figure 2; electronic supplementary material, A). It turns out that some of these differences can be traced to global patterns of behaviour. 1.0 0.5 0 –0.5 –1.0 –1.5 0 5 10 15 hours in an average day 20 Figure 11. Deviation from the average number of directed mentions (a) and shared hashtags (b) between the European and Asian longitude ranges during an average day in units of standard deviations (Z-score). Grey shadowed regions represent the synchronized times. homogenization in habits and customs among globally differentiated cultures and social contexts. Furthermore, there is a specific synchronization in figure 5 that is actually a global phenomenon. Distinct from the other behaviours that track the daily period and therefore are diagonal, between longitudes 08 and 1808, a horizontal line (black) shows a simultaneous peak of activity that occurs daily across the European, Asian, African and Oceanian continents. This horizontal peak reflects large-scale dependencies across half of the world. The synchronization of activity is manifest in a dynamic correlation network between nodes representing cities, whose edges appear when the urban time series are correlated above a given threshold (r . 0.9). Correlations are calculated by using overlapping time windows of 12 h across the cities’ average day time series. Highly synchronized cities have stronger connections with each other than with the rest of the network. In figure 10b,c, we show two snapshots of the correlation network at different times. Cities are generally linked within times zones, because it is natural for cities to be synchronized to those in similar longitudes (figure 10b). However, at the time of global synchronization (figure 10c) cities across Eurasia and Africa are strongly coupled, manifesting their synchronous activity. Such global synchronization can be expected to arise in the context of increasing global interactions consistent with synchronization in many complex systems [39]. For additional evidence that synchronization arises from social interactions, we studied directed messages in the content of tweets (mentions) and topic identifiers (hashtags) between the European and Asian longitude ranges (figure 11). We a = 0.0 a = 0.2 a = 0.4 a = 0.6 a = 0.8 a = 1.0 9 0 b = 0.8 0.2 0.4 b = 1.0 0.6 (b) (i) 0.8 1.0 (ii) 0 time 5 10 15 20 longitude active cities Figure 12. (a) Model outcomes for multiple values of intercity influence at multiple longitudes (a) and night activity (b) with the same initial conditions. Longitudes are represented in the x-axis and universal time is represented in the y-axis (see (b)(i) for scale). Colours indicate the level of activity (scale shown in figure). We normalize the cities’ activities by their maximum value. (b) Average model outcomes after introducing the effects of large inactive areas—oceans. Panels (b)(i) and (b)(ii) show inactive areas at different locations. Parameters a ¼ 0.4 and b ¼ 0.2. The blue series indicates the number of active cities (x-axis) at each time of the day ( y-axis). Colour scale is similar to top panels. found that the number of interurban directed messages and common hashtags simultaneously peak during the synchronized time. At this time a significantly larger number of directed messages are sent between these regions and more hashtags are shared in their messages with respect to other times of the day ( p , 0.001). These results indicate that people tend to share more information about increasingly similar topics as they synchronize their activities. We model the global synchronization process with an iterative dynamical model based on the tendency of tweets to trigger other tweets. The full model includes the tendency of people to tweet before going to bed and absence of tweets at night. The model is defined by the iterative map in the changing daily dynamics of a city: X X si ðs,tÞ ¼ si ðs,t  1Þ þ a sj ðs,t  1Þ þ b dðs  sb Þ, j=i sb ð4:1Þ where si represents the temporal activity of city i, s [ [0, 23] indicates time of the day, t represents day-to-day changes, which is our iterative variable (we ignore weekend differences for this purpose), and sb indicates the locationdependent time of evening activity. Parameters a [ [0, 1] and b [ [0, 1] indicate the weights of intercity influence at multiple longitudes and evening activity, respectively. Activity is set to zero between times 0 , s , 8. We normalize P si (s,t) at each iteration so that s si ðs; tÞ ¼ 1. At t ¼ 0, si (s) is set to random values. In figure 12a, we present the outcomes of the model for multiple values of intercity influence (a) and evening activity (b). The initial conditions vary among cities but do not change for different a and b configurations. The blue diagonals indicate local sleeping times. If a ¼ b ¼ 0, the model results in an independent random distribution of activities among cities. For positive values of a, cities are able to influence each other and horizontal stripes emerge, indicating the synchronization of activities in cities at multiple longitudes. The horizontal stripes emerge at the times where the sum of initial conditions is slightly higher and therefore symmetry breaks. Similarly, higher values of b result in peaks of activities before sleeping time (red diagonals). Both behaviours are simultaneously found for intermediate values of these parameters (i.e. a ¼ 0.4 and b ¼ 0.2). We add an inactive ocean to the model in figure 12b and average over 100 realizations of two specific parameter values. The inactive areas affect the number of active cities at each time of the day. As a result, the synchronized peaks of activity (red horizontal stripes in squared panels) emerge at the times where most of cities are active (blue curve in rectangular panels) and consequently the sum of initial J. R. Soc. Interface 14: 20161048 b = 0.6 b = 0.4 b = 0.2 rsif.royalsocietypublishing.org b = 0.0 (a) 5. Conclusion Authors’ contributions. All authors contributed in making the figures and writing the manuscript. Competing interests. We declare we have no competing interests. Funding. This study was funded by NECSI internal funds. Acknowledgements. We thank Richard J. Cohen for helpful comments and discussions. References 1. Bettencourt LM. 2013 The origins of scaling in cities. Science 340, 1438 –1441. (doi:10.1126/ science.1235823) 2. Pentland A. 2014 Social physics: how good ideas spread—the lessons from a new science. New York, NY: Penguin Press. 3. Libert B, Wind Y, Fenley M 2014 What Airbnb, Uber, and Alibaba have in common. Harvard Business Review. 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