Tommaso Venturini

Kari De Pryck

Robert Ackland

Bridging in Network Organisations the Case of International Panel on Climate Change (IPCC)

In this paper, we investigated the relational architecture of the Intergovernmental Panel on Climate Change focussing on the individuals that, in the thirty years of existence of the IPCC, have assured the connection between the different temporal, thematic and functional divisions of the organisation. To identify these bridge individuals, we proposed a new measure of bipartite bridgeness defined as the summation of the inverse Jaccard similarity coefficient of the neighbourhoods of all pairs of divisions to which an individual has participated. As we illustrated using an original database of the eight thousand individuals who contributed to the IPCC since its foundation, this measure of bipartite bridgeness is more informative than the simple degree, as it takes into account the importance and the rareness of the connections assured by each bridge.

Introduction

It is a defining claim of social network analysis [START_REF] Scott | Social Network Analysis[END_REF][START_REF] White | Identity and Control. A Structural Theory of Social Action[END_REF][START_REF] Freeman | The Development of Soical Network Analysis[END_REF] and more generally of relational sociology [START_REF] Tarde | Les empêcheurs de penser en rond[END_REF][START_REF] Emirbayer | Manifesto for a Relational Sociology[END_REF][START_REF] Latour | Reassembling the Social. An Introduction to Actor-Network-Theory[END_REF] that the essence of collective phenomena lies not in external structures but in the internal connections between their parts. This claim is easier to defend when studying dynamics and change, but more difficult when considering continuity and persistence, which, in social sciences, are traditionally associated with macro-structures. The decisive test for relational sociology is therefore to explain the continuity of social organisation and account for the stable empirical regularities that, since Durkheim, represent the bedrock of structural sociology. In contrast to Durkheim's Rules of Sociological Method (1884[START_REF] Durkheim | The Rules of Sociological Method (Translation[END_REF], we need to ground continuity and persistence not on the "solid foundation" of structures but on "shifting sand" of relations1 and show that collective phenomena are in the whole because they are in the parts and not in parts because they are in the whole2 . social structure, etc. As these forms exist permanently and do not change with the various applications which are made of them, they constitute a fixed object, a constant standard which is always to hand for the observer, and which leaves no room for subjective impressions or personal observations… In order to proceed methodically we must establish the prime bases of science on a solid foundation, and not on shifting sand." (pp. 82-83, Durkheim, 1884(pp. 82-83, Durkheim, (1982 translation) translation), emphasis added).

As an example of this challenge, we propose in this paper to inquire into the peculiar organisation of the Intergovernmental Panel on Climate Change (IPCC). The IPCC is a fascinating institutional puzzle. Despite its gruelling mission -building a consensus on climate change in the academic community and between world governments -the IPCC has prospered as few expert organisations before. While not exempt from criticisms [START_REF] Lidskog | When Does Science Matter? International Relations Meets Science and Technology Studies[END_REF], the IPCC has thrived steadily and under all respects. In its thirty-year existence, the IPCC produced five assessment reports (ARs) whose length has grown from the 1,222 pages of the first assessment report to the 5,021 pages of the last; the number of its authors has quadrupled (from 437 to 1887); the number of national delegates almost tripled (from 590 to 1569). The growth of the IPCC has not only been quantitative. In each successive report, the IPCC has strengthened its authority in the climate debate and consolidated its position at the interface between scientific research and diplomatic negotiations to the point of being awarded the Nobel Prize for Peace in 2007. The IPCC success has also inspired the creation of several other global environmental assessments including the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (often described as the IPCC for biodiversity).

Remarkably, this expansion has not been accompanied by an institutional hardening. Apart from a secretariat of a dozen members, the IPCC has no permanent organs and no stable employees. All of the eight thousand individuals who contributed to its assessment reports did it on a voluntary basis and on the payroll of other institutions. Unlike other international organisations (Reinalda & Verbeek eds., 1998), the IPCC has not entrusted its activities to a group of hired bureaucrats. Instead it has remained a "network-organisation" (cf. [START_REF] Corbera | Patterns of Authorship in the IPCC Working Group III Report[END_REF] most of whose contributors are replaced at every assessment cycle and maintain their primary affiliation to other institutions.

The stabilisation of the IPCC in the international climate regime [START_REF] Hughes | Bourdieu and the IPCC's Symbolic Power[END_REF], we contend, is not due to the establishment of hard institutional structures, but to the complex dovetailing of its practice fastened by the relational glue provided by individuals who served in multiple parts of the organisation. We call these individuals "bridges" following IPCC's own terminology, but also because the term resonates with a central theme in social networks analysis. It is known that graph theory itself was initiated by Leonhard [START_REF] Euler | Solutio Problematis Ad Geometriam Situs Pertinentis[END_REF] to solve the puzzle of the bridge of the city of Königsberg and since then the notion of bridges between different network regions has received sustained scholarly interest -especially in its application to social phenomena. Jacob Moreno (the father of social network analysis), for instance, dedicated particular attention to identifying the nodes connecting distant regions of his "sociograms" [START_REF] Moreno | Who Shall Survive?[END_REF]). Yet, it is with the influential paper of Mark Granovetter on The Strengh of Weak Ties (1973) that the importance of social bridges came into full view. Central to the paper is the idea that weak ties are crucial relational assets precisely for their capacity to connect distant social worlds. The same idea is developed by Ronald [START_REF] Burt | Brokerage & Closure: Introduction to Social Capital[END_REF] who highlights the importance of brokering nodes "connecting across clusters to engage diverse information" (Burt et al. 2013, p. 530). In a different tradition, Luc [START_REF] Boltanski | L'espace Positionnel : Multiplicité Des Positions Institutionnelles et Habitus de Classe[END_REF] argued that "multipositionality" -the property of occupying multiple positions in different social fields -is a crucial source of social capital (see also a network analysis of this phenomenon in [START_REF] Venturini | Hors Champs: La Multipositionnalité Par l'analyse Des Réseaux[END_REF] and similar observation has been made about corporate interlocking [START_REF] Allen | Interlocking Corporate Directorates[END_REF].

In this paper we develop these ideas using the case study of the individual bridging between the different components of the IPCC. Through this analysis, we pursue two objectives. First, we hope to contribute to the understanding of an organisation that is increasingly taken as an example of cooperation between countries and between scientists and policymakers. Second, we propose a new measure of bridgeness in bipartite networks (i.e. two-mode graph that contain two types of nodes and where edges only connect nodes of different types, cf. [START_REF] Borgatti | Network Analysis of 2-Mode Data[END_REF][START_REF] Borgatti | Network Analysis of 2-Mode Data[END_REF][START_REF] Guillaume | Bipartite Structure of All Complex Networks[END_REF][START_REF] Guillaume | Bipartite Structure of All Complex Networks[END_REF].

The IPCC as a complex organisation

While bridging is a node-level property that can be measured in any network, we are in this paper particularly interested in bridging in complex organisations -that is, organisations that are composed of subparts which differ in several respects. The IPCC is clearly one such organisation, as its institutional architecture is characterised by a temporal, functional and thematic differentiation.

First, its activities are not carried out as a constant process, but divided in "assessment cycles", each driven by a different leadership and a specific thematic outline. Each assessment is also divided in different phases (definition of the outline, election of the leadership, selection of the authors, writing and reviewing of drafts, distillation of summaries, etc.) and punctuated by yearly or bi-yearly summits, which constitute the only physical meeting between IPCC contributors.

Second, the IPCC is a hybrid organisation, characterised by the cohabitation of scientists coming from different disciplines and diplomats representing different countries. Not only do these two populations often have different professional backgrounds, but they serve different functions in the IPCC: while the authors are tasked with reviewing and summarising climate change literature, the delegates are in charge of managing the process and making sure that the academic outcomes are translated to the policy community [START_REF] Pryck | Intergovernmental Expert Consensus in the Making. The Case of the Summary for Policymakers of the IPCC 2014 Synthesis Report[END_REF].

Third, IPCC assessment reports are divided into three volumes each produced by a dedicated thematic "Working Group" (WG): WG1 focuses on the physical basis of climate change; WGII on impacts, adaptation and vulnerability and WGIII on mitigation. Because of this specialisation, the working groups tend to be composed of scientists coming from different disciplines, with a prevalence of climatologists in WGI, biologists and demographers in WG2 and economists and engineers in WGIII. Each working group is led by two co-chairs and has access to a dedicated Technical Support Unit. Besides the volumes produced by the three working groups, IPCC reports also contain (from AR2 on) a Synthesis Report (SYR), which combines the results of the three other volumes. Each volume is also composed of different chapters (whose number varies from 7 in AR1-WG2 to 30 of AR5-WG2), but this further thematic subdivision is not considered in this paper.

To investigate the bridges connecting the different components of the IPCC, we collected the names of all the individuals who have contributed to the first five assessment reports of the IPCC3 . We put great effort to disambiguate homonyms and to merge different names of the same person, but errors may remain. Our database contains about 18,000 rows, each corresponding to a given individual contributing in a given capacity. The 24 capacities we considered are defined by the combination of the temporal, functional and thematic divisions of the IPCC, as illustrated in table 1: Table 1

. Temporal, functional and thematic divisions of the IPCC and the capacities they form

Using a tool called Table2Net4 , we extracted from our database a bipartite network, whose two modes are the capacities presented above (coloured nodes in fig. 1) and the individuals that have contributed to them (grey nodes). The dark grey nodes are our bridges -individuals that connect the different divisions of the IPCC through their varied contributions. The IPCC's procedures (ipcc.ch/scoping_meeting_ar5/doc10.pdf, p. 10) explicitly identify bridges as those authors who deal "with cross-cutting topics across WGs" in the same AR. Beside these thematic bridges, we extended the IPCC's definition to consider also functional bridges, individuals who have served as both author and delegate in the same AR; and temporal bridges, individuals that have participated in more than one AR while having the same function within the same WG (the SYR being considered as a WG for the purpose of this paper).

For reasons that we will explain in the next section, we do not consider mixed bridges, i.e. individuals that have participated in different ARs in different functions or different WGs. According to this definition, our network contains 1,198 bridges, amounting to more than one fifth of the total of 5,676 contributors in our dataset5 . Edges are weighted according to the number of times that each individual has served in the same capacity (for example, authoring two different chapters within the same WG report during the same AR). Before moving to the mathematical analysis, a visual inspection of the network above yields some interesting insights. The network in fig. 1 has been spatialised with a force directed layout [START_REF] Jacomy | ForceAtlas2, a Continuous Graph Layout Algorithm for Handy Network Visualization Designed for the Gephi Software[END_REF], which draws closer the nodes with more direct (and indirect) connections between them, and pushes away nodes that are less connected to one another. This means that spatial proximity is a good indicator of structural grouping [START_REF] Venturini | Social Science Research Network What Do We See When We Look at Networks an Introduction to Visual Network Analysis and Force-Directed Layouts[END_REF]. The clustering in the figure appears to reflect above all the functional division of the IPCC (with authors and delegates located respectively in the upper and lower part of the network), but also the thematic division (with a clear separation between the three WGs6 ). We coloured the nodes according to these divisions precisely to highlight the fact that they do not mix in the figure. It is interesting that the only mixing concerns the capacity "ar1-author-wg3", which is positioned very close to the delegates cluster. This offers a confirmation of our method, because in the first assessment cycle, the WG3 was mandated with the highly politicised task of formulating response strategies to climate change and involved many government officials and negotiators [START_REF] Tora | Structure and Agent in the Scientific Diplomacy of Climate Change[END_REF].

It is also interesting to notice the middle position occupied by the SYR of AR2, which is distinctively closer to the delegates than the other Synthesis Reports, this can be explained by the fact that in its first edition (the SYR being introduced in AR2), the Synthesis Report was authored mostly by members of IPCC Bureau many of whom were also part of their national delegation.

In contrast to the high functional and thematic clustering, the temporal articulations of the IPCC in different ARs does not seem to produce much clustering, as nodes of the same AR are generally far one from another7 . This means that there are more bridges between the same functions or themes in different ARs, than between different functions or themes in the same AR. The prevalence of temporal bridging is even more evident if we transform our bipartite graph into a monopartite one in which the different capacities are connected by edges weighted by the number of individuals that they have in common. In figure 2, the edges between different pairs of capacities are sized according to their weight and coloured by their type. The temporal bridge edges (blue) are significantly thicker (reflecting the fact that more individuals are fulfilling this type of bridging), compared with the functional bridge edges (green) and thematic bridge edges (red). This prevalence of temporal bridging is also confirmed by looking at the composition of bridging individuals. Our dataset contains 1088 temporal bridges (individuals who have participated in the same function -delegate or author -in two or more ARs, compared with only 255 functional bridges (individuals who participated as both delegate and author in the same AR) and 143 thematic bridges (individuals who participated as authors in two or more WGs in the same AR) 8 . The first finding of our analysis is therefore that the one type of bridging explicitly acknowledged in IPCC procedures, the thematic one, is by far the least common in our dataset9 .

A measure of bipartite bridgeness

Having examined how the IPCC capacities are connected to one another through bridging individuals, we can move to consider the other 'mode' of our bipartite network, that is to say the individual contributors. The objective here is to identify which individuals are most important in bridging the different divisions of the complex organisation that is the IPCC. Using the classic measure of betweenness centrality [START_REF] Freeman | Your Use of the JSTOR Archive Indicat[END_REF][START_REF] Brandes | A Faster Algorithm for Betweenness Centrality[END_REF] is not fully satisfying here, because this solution does not take into consideration the "bipartite" nature of our graph. Drawing on the fact that, in bipartite networks, nodes of the same type are never directly connected, we propose to measure the bridgeness of a node as a function of the inferred or imputed connections that it creates among the nodes of the other type. The simplest way to implement this idea is to define the bipartite bridgeness of a node 𝛼 of type A as the number of pairs of nodes of type B nodes that have inferred connections due to the linking activity of 𝛼. This number is the equal to the number of unique combinations of unordered pairs of 𝛼's neighbours, and is therefore directly related to the degree of 𝛼:

𝑝𝑎𝑖𝑟𝑠 𝑜𝑓 𝑛𝑜𝑑𝑒𝑠 𝑏𝑟𝑖𝑑𝑔𝑒𝑑 𝑏𝑦 𝛼 = 𝑑𝑒𝑔𝑟𝑒𝑒(𝛼)! 2! * (𝑑𝑒𝑔𝑟𝑒𝑒(𝛼) -2)!
This measure, however, considers each act of bridging as equivalent and discounts the fact that different B-nodes can have different importance as well as the fact that some inferred connections between B-nodes will be more uncommon than others. To take these two elements into consideration, we propose an alternative definition of the bipartite bridgeness of a node 𝛼 of type A as the number of pairs of nodes of partition B that it bridges, weighted by: (1) the total number of neighbours of the two bridged B-nodes and (2) the inverse of the number of A-nodes bridging the same pair. In other words, we define the bipartite bridgeness of 𝛼 as the summation for each pair i, j bridged by 𝛼 of the size of the union of their neighbours divided by the size of the intersection of their neighbours.

𝐵𝐵(𝑛) = 8 !,# | 𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑢𝑟𝑠(𝑖) ∪ 𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑢𝑟𝑠(𝑗) | | 𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑢𝑟𝑠(𝑖) ∩ 𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑢𝑟𝑠(𝑗) | = 8 !,#

𝐽𝑎𝑐𝑐𝑎𝑟𝑑(𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑢𝑟𝑠(𝑖), 𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑢𝑟𝑠(𝑗))

8 Note that the sum of these different types of bridges is greater than the total number of bridges (1,198) because the same individual can bridge the organisation in different ways. In fact, the prevalence of temporal bridging is also indicated by the fact that most of the functional and thematic bridges are also temporal bridges (only 81 and 34, respectively, are not) while most temporal bridges (861) are only temporal.

The size of the intersection of two sets divided by the size of their union is commonly known as the Jaccard coefficient of those two sets, and hence bipartite bridgeness can be defined as the summation of the inverse Jaccard similarity coefficient of the neighbourhoods of all pairs of neighbours of 𝛼. The fact that the Jaccard similarity coefficient is a classic measure of similarity between sets provides intuitive support for our bipartite bridgeness measure since we want to capture not only the number of pairs bridged by the node 𝛼, but also their relational diversity10 .

In figure 3 below, the node 'ε' has a bridgeness of 7, which comes from being the only bridge between 'a' and 'b' (size of union is 2, size of intersection is 1) and between 'a' and 'c' (size of union is 3, size of intersection is 1). ε also bridges the pair 'b' and 'c' (size of union is 4, size of intersection is 2) but shares this bridging with another node (hence the division by 2). In our IPCC network, the bipartite bridgeness of each individual is then the summation, for each pair of capacities bridged by that individual, of the total number of the individuals who served in either of the two capacities (i.e. the size of the union of the capacities' neighbourhood in the bipartite network) divided by the number of individual who served in both (i.e. the size of the intersection of their neighbourhood). Being defined as a summation over the pairs of capacities bridged by an individual, our measure is strongly correlated to the degree of the individual in the bipartite network. Yet, because it also takes into consideration the total number of individuals participating in the two capacities (in its numerator) and the rarity of overlaps of individuals i.e. their bridges (in its denominator), it offers a more nuanced way of identifying the individuals occupying key bridging positions in our complex organisation.

imagined by Granovetter in the article cited in the introduction of this paper:

Consider, now, any two arbitrarily selected individuals-call them A and B-and the set, S = C, D, E, ... , of all persons with ties to either or both of them. The hypothesis which enables us to relate dyadic ties to larger structures is: the stronger the tie between A and B, the larger the proportion of individuals in S to whom they will both be tied, that is, connected by a weak or strong tie. This overlap in their friendship circles is predicted to be least when their tie is absent, most when it is strong, and intermediate when it is weak. [START_REF] Granovetter | The Strength of Weak Ties[END_REF](Granovetter, , p. 1362)).

The diversity of the three types of bridging is illustrated in the table by the fact that most contributors are only present in one ranking (the white background cells). Among the contributors that feature as top bridges according to different types of bridging, we found for example Linda Mearns (senior climate scientists at the US National Center for Atmospheric Research) who has bridged between WG1 and WG2 in three following cycles, AR3, AR4 and AR5 (and is also active in the current AR6) and Michael Grubb (Professor of Energy and Climate Change at University College London), who has bridged WG1 and WG3 in AR2 as well as WG2 and WG3 in AR4. Looking at the table, we can also observe that Bureau members tend to be higher ranked as functional bridges than as thematic or temporal bridges. This is not surprising as, in order to be elected as Bureau members, contributors need to have credible scientific credentials but close ties with the national delegation that nominates them.

Another way of making similar observations is projecting the values of our bipartite bridgeness on the network of figure 1, by varying the size of the nodes representing the contributors according to their bridgeness score. Looking at figure 5 above, it is easy to observe that the contributors with the highest bridgeness are positioned in the bottom of the figure. This indicates that the most important bridges tend to be also delegates. The bridges that are also members of the IPCC Bureau (the red nodes) are positioned particularly close to delegate capacities. This captures an old tradition of the IPCC: in the first assessment reports, most members of the Bureau were also head of their national delegation. In the latest ARs, this is no longer the case, but the members of the Bureau are still supposed to represent their countries (as well as the geographical regions of their countries) and are often listed among the members of their national delegations in official documents (and hence in our database). It is also interesting to note that the five scientists that have so far served as Chair of the IPCC (Bert Bolin, Robert Watson, Rajendra Pachauri and Hoesung Lee) are all very visible as bridges and positioned close to the ARs that they chaired.

A closer examination of figure 5 also reveals that the bridges tend to be positioned toward the left, suggesting that more bridging is performed in the later assessment cycles than in the earlier. This is, to some extent, a simple effect of the increase in the size of the IPCC, but it also derives from the effort of the organisation to encourage its contributors to serve in different capacities and connect its different divisions. A way to test this idea is to count the number of functional and thematic bridges active in the different assessment cycles (Table 4)11 . In Table 4, darker cell colours indicate higher numbers, and this makes it easy to observe the general increase in the number of bridging actions (both in functional and thematic bridging) in successive assessment reports -though with an interesting reduction in functional bridging between AR4 and AR5 and in thematic bridging between AR3 and AR4. Since our dataset contains information on not only in which IPCC capacities different individuals have participated in but also their country of affiliation during each participation12 , we can aggregate the values of bridgeness by country and country groups. Table 5 shows the number of individual bridges and the sum of their bridgeness for different countries of different development status and regions (according to the official classification of the World Meteorological Organisation used in the IPCC). It is important to note that, in order to avoid double counting, we excluded from the sums of table 5, all individuals who were affiliated to different countries in different assessment reports. Table 5 shows that, despite having a smaller number of total contributors, developed countries have more bridges and a much larger sum of bridgeness compared with developing countries. This confirms the dominance of developed countries in the IPCC and in climate science in general [START_REF] Corbera | Patterns of Authorship in the IPCC Working Group III Report[END_REF]. Similarly, when looking at regions, we can observe a clear dominance of Europe (both for number of bridges and sum of bridgeness) followed by Asia and North and Central America. The very good result of Asia is confirmed by the fact the current Chair of the IPCC (Hoesung Lee) is a scientist from South Korea and the previous one (Rajendra Pachauri) from India.

Aggregating the same information by country (table 6 and figure 7) reveals an extremely skewed distribution of bridgeness in the IPCC. While such unevenness is to a large extent a simple consequence of the unequal number of IPCC contributors by country, the skewness is considerably higher for the bridgeness (the top-10 countries for bridgeness control more of this variable than all the other countries together, compared to the top-14 for number of bridges and top-19 for number of contributors). This suggests that the dominance of some countries in the IPCC may be even greater than may appear by looking just at the number of contributors, as these countries seem to control most of the key bridging positions in the organisation.

Conclusion

In this paper, we investigated the relational architecture of a particularly influential organization in the international climate regime: the Intergovernmental Panel on Climate Change (IPCC). The IPCC is an interesting case study not only for its crucial role of "trading zone" [START_REF] Collins | Trading Zones and Interactional Expertise[END_REF] between the sciences of climate change and national and international policymaking, but also for its capacity to survive and prosper for more than thirty years despite its relatively light institutional structures. The IPCC produces its expert assessments, drawing on the voluntary contributions of a multitude of participants who maintain their primary affiliation to other institutions and are, in most cases, replaced at every new assessment cycle.

Besides its institutional practices and bureaucratic procedures, the IPCC owes its continuity and persistence to the individuals that remained in the organisation for several assessments, or that served in more than one of its working groups, or who contributed to its operations simultaneously as scientific experts and as national delegates. These bridge individuals play a crucial role in the IPCC stabilizing its complex architecture and gluing together it's different (and otherwise quite independent subparts).

To identify these bridge individuals, we proposed a new measure of bipartite bridgeness defined at the as the summation of the inverse Jaccard similarity coefficient of the neighbourhoods of all pairs of neighbours of a given node. As we illustrated using a database of the eight thousand individuals who contributed to the IPCC since its foundation, this measure of bipartite bridgeness is more informative than the simple degree, as it takes into account the importance and the rareness of the connections assured by each bridge. Using this measure, we investigated the IPCC as a network-organisation and inspected the individuals the temporal, thematic and functional bridging of its divisions. Besides the IPCC, our measure and the protocol that we employed to investigate bipartite bridges can, we believe, be fruitfully applied to other complex organisations that can be represented as bipartite networks of contributors and subparts.

Figure 1 .

 1 Figure 1. Bipartite network of the IPCC contributors and the capacities in which they have served (capacities are coloured according to their functional and thematic division; bridges are dark grey nodes)

Figure 3 .

 3 Figure 3. Simple examples of calculation of bipartite bridgeness.

Figure 5 .

 5 Figure 5. Bipartite network of the IPCC contributors (grey) and the capacities in which they have served (coloured according to their functional and thematic division). The nodes representing the contributors are sized according to their bipartite bridgeness score and coloured in red if they are members of the IPCC Bureau and in grey if they are not. Labels are shown only for the 140 contributors whose bridgeness is higher than 1300.

Figure 6

 6 Figure 6 illustrates the number of temporal bridging actions between different ARs, with the increasing thickness of arcs connecting pairs of ARs from left to right indicating an increase in bridging with time.

Figure 6 .

 6 Figure 6. Bridging actions between different ARs.

Table 2

 2

. Most intensely bridged capacity pairs Figure 2. Monopartite graph of IPCC capacities. Edges are coloured by type of bridging and weighted by the number of common contributors.

Table 4 .

 4 Number of functional and thematic bridging actions between different capacities over the five assessment cycles (darker background indicates higher numbers).

Table 5 .

 5 Sum of bridgeness, number of bridges and number of contributors by development status and WorldMeteorological Organisation geographical regions.

	Country groupings	Bridgeness Sum	Bridges No.	Contributors No.
	Developed Countries	30.5154	591	2.444
	Developing Countries	20.7877	507	2.828
	Economies in Transition	21.102	50	278
	Region I (Africa)	51.030	157	806
	Region II (Asia)	115.656	253	1.430
	Region III (Sud America)	31.080	67	361
	Region IV (Nord and Central America)	99.745	202	924
	Region V (Sud-West Pacific)	33.627	75	398
	Region VI (Europe)	186.860	361	1.575

Table 6 .

 6 Total

		Bridgeness	Bridges	Contributors
	Countries	Sum	No.	No.
	USA	65820	109	499
	UK	32095	47	175
	China	31180	66	219
	Japan	22077	53	317
	Australia	19275	33	116
	Germany	17524	35	178
	Netherlands	17267	35	87
	India	15856	23	99
	Canada	14821	39	141
	South Korea	11985	21	203
	France	11860	26	115
	Brazil	11836	19	102
	Saudi Arabia	10995	20	113
	Argentina	10479	13	57
	Denmark	10299	11	45
	Sweden	9852	11	50
	Cuba	9066	8	18
	Russian Fed.	8739	12	50
	Switzerland	8725	10	50
	Italy	7458	11	52

bridgeness, number of bridges and number of contributors for the 20 countries with the highest total bridgeness. Figure 7. Bar chart of the total bridgeness for all the countries participating to the IPCC.

"Collective habits are expressed in definite forms such as legal or moral rules, popular sayings, or facts of

"if [a phenomenon] is general it is because it is collective (that is, more or less obligatory); but it is very far from being collective because it is general. It is a condition of the group repeated in individuals because it imposes itself upon them. It is in each part because it is in the whole, but far from being in the whole because it is in the parts." (p. 56, Durkheim, 1884" (p. 56, Durkheim, (1982 translation) translation), emphasis added)).

The dataset described in this paper has been initiated thanks to the support of the ANR project MEDEA and about half of it completed at the médialab of Sciences Po, through the work of Ian Gray, Nicolas Baya Laffite and Audrey Banneyx, which we greatly thank for their contribution.

http://tools.medialab.sciences-po.fr/table2net/

It is important to note that our network only includes Contributing Leading Authors, Leading Authors or Reviewers (i.e. only the authors with roles of coordination and responsibility and who are directed selected by the IPCC Bureau). We have not considered Contributing Authors (who are invited to submit written contributions to specific paragraphs in the reports chapters) because, while their contribution is scientifically important, the fact that they do not participate in the author meetings of the IPCC diminishes their importance as organisational bridges. The edges of the graph represent the contribution of each individual.

As expected, the SYR authors are consistently positioned between the three working groups, reflecting their role in providing a synthesis of the working groups.

Note however that in each WG cluster and in the cluster of delegates, the ARs tend to be ordered chronologically from right to left, which indicates that more bridges exist between temporally adjacent ARs.

This finding depends, at least in part, on the fact that our definition of bridging is very strict and only takes into consideration authoring contributions in coordinating or reviewing roles. Accordingly, in this study, thematic bridges tend to be scientists with significant expertise in two or more disciplinary sectors, which is by definition very rare. A more common (but weaker) way of connecting two WGs is to participate as coordinating or reviewing author in one group and only as contributing author in the other.

Note that our measure of bipartite bridgeness is also a direct implementation of the idea of "weak ties"

To be precise, since the same person can serve as two different types of bridges during the same AR, table4indicates the number of "bridging actions" rather than the number of individual bridges.

The country of affiliation does not necessarily correspond to the nationality of individuals but indicated instead the nationality of their institution or the country that they were representing.

Discussion and results

Quantitative evidence of the analytical value of our measure comes from the comparison with another piece of information which we have not yet considered. In table 1, we purposely omitted another crucial role in the IPCC: that of Bureau members. The Bureau supervises the work of the IPCC and its members are selected by the Member states at the beginning of each evaluation cycle.

Because we did not include the information about Bureau membership in our network, we can now use this information to validate our measure of bipartite bridgeness. Because Bureau members are officially in charge of coordinating the work of the IPCC, we expect them to have a higher bridging score than other IPCC members because first, their election is facilitated by a long and varied engagement with the organisation and second, because their role necessitates their involvement in different divisions of the organisation. Indeed, we find that the proportion of Bureau members that are also bridges (in the sense that they have a bridging score higher than zero) is much higher than the proportion of non-Bureau members: 84% against 20%. Even by focussing exclusively on the subpopulation of Bureau members and non-Bureau members that are bridges, both the mean and the median of bipartite bridgeness is considerably higher for Bureau (mean-BB = 1717 and median-BB = 1139) than for non-Bureau (mean-BB = 357 and median-BB = 96).

It is also possible to use the information about Bureau membership as evidence that our measure is more informative than the simple measure of degree in the bipartite network. Indeed, Bureau members generally rank higher when IPCC contributors are sorted by bipartite bridgeness, than when they are sorted by degree. The average ranking for Bureau members is 729 when ranked by bipartite bridgeness and 880 when ranked by degree (and 220 against 297 when only contributors with a bridging score higher than zero are considered).

Another, more qualitative, way of comparing bipartite bridgeness with degree comes from identifying the most important actors by each measure. Figure 4 displays the top-54 contributors by bridgeness (bridgeness > 1080) and by degree (degree > 5) in a bridgeness VS degree scatterplot. In the quadrant that contains contributors that are top-ranked only according to bridgeness (top-left), we find people who played crucial roles in the IPCC and that would have not been highlighted by degree alone. For instance, we would miss Taha Zatari and Yuri Izrael, who, despite having a degree of only 4 and 5 respectively, have been highly influential contributors to the IPCC as Bureau members and long-standing members of their delegation (respectively Saudi Arabia and the Russian Federation).

So far, we have worked with a general definition of bridgeness that does not discriminate between the three different types of bridging discussed above. It is however not difficult to decompose such general measure into its thematic, functional and temporal components. Table 3 below displays the top-25 bridges by types of bridging.


Maria Castaldo

Tommaso Venturini

Paolo Frasca

Floriana Gargiulo
email: floriana.gargiulo@cnrs.fr

The Rhythms of the Night: increase in online night activity and emotional resilience during the Spring 2020 Covid-19 lockdown

published or not. The documents may come     The Rhythms of the Night: increase in online night activity and emotional resilience during the Spring 2020 Covid-19 lockdown

Introduction

The lockdown established in France from March 17th to May 11th as a response to the Covid-19 pandemic created a sudden and severe transformation of daily routines. This disruption represents a textbook case of exogenous shock on human behaviors, which can, by comparison, reveal features of normal social life. In this paper we carry out this comparative analysis, focusing on online behaviors and leveraging a unique YouTube dataset. A few weeks before the lockdown, we had started following a corpus of more than one thousand French political YouTube channels with an exceptional temporal granularity -recording hour by hour the number of views of all of their videos. This collection provided us with a unique dataset to study how the lockdown transformed the circadian rhythms of online activities. To make sure our findings are not platform specific, we compare the results obtained on YouTube with a Twitter dataset of 8 million tweets in French.

In this paper, we investigate changes in the daily rhythm of online activities and address two related research questions: what are the changes produced by the lockdown and how resilient are online circadian rhythms. The analysis of such a exceptional period allows us to distinguish the dynamics due to the Covid-19 crisis from stable features of the social media we investigate. We focus our research on a single country, France, in order to identify precisely the start and end dates of the lockdown and to work on a (relatively) uniform population sample that excludes national differences.

Our analysis shows, for both platforms, an increase of online activities, likely a consequence of the decrease of real-life interactions. The growth in online participation and content consumption is not uniform across the 24 hours, but it is more salient during the night. Besides this variation in volume, we register changes in the kind of content shared from an emotional and thematic point of view. In both platforms, the lockdown is marked by an unexpected decrease in emotional contents and by a more predictable thematic shift from topics like "social life" and "leisure", before the lockdown, to matters related to "house" or "death" during the lockdown. Against these lockdown-induced changes, some constants of YouTube and Twitter stand out. Despite its quantitative change, the shape of the daily cycle of different emotions (i.e. their prevalence by hour) is not impacted by the lockdown: this finding confirms the results of previous studies that showed a stability of emotional rhythms across seasons and cultures [START_REF] Golder | Diurnal and seasonal mood vary with work, sleep, and daylength across diverse cultures[END_REF][START_REF] Dzogang | Circadian mood variations in Twitter content[END_REF][START_REF] Lampos | Analysing mood patterns in the United Kingdom through Twitter content[END_REF]. The resilience of these patterns, despite the disruption of the lockdown, may be due to biological origins of the emotional expression, which seems to be more influenced by the biological clock than by exogenous factors.

Related Work

The patterns of activity in different social media vary according to the characteristics and the scope of the different platforms and to the composition of its user pool. Several papers in the literature have studied circadian fingerprints in different social media. In YouTube, scholars have investigated the rhythms of content creation (i.e. video posting) [START_REF] Szabo | Predicting the popularity of online content[END_REF] and of content fruition (i.e. videos watching) [START_REF] Gill | Youtube traffic characterization: a view from the edge[END_REF]. Daily and a weekly use of Twitter has been analyzed in various countries [START_REF] Ten Thij | Circadian patterns in Twitter[END_REF]. Among other platforms, Foursquare has attracted researchers' attention for its circadian and geographic patterns [START_REF] Noulas | An empirical study of geographic user activity patterns in Foursquare[END_REF] and its similarities with Twitter [START_REF] Grinberg | Extracting diurnal patterns of real world activity from social media[END_REF], while Wikipedia editing patterns have been studied in [START_REF] Yasseri | Circadian patterns of Wikipedia editorial activity: A demographic analysis[END_REF] with an interesting focus on inter-cultural variations. Moreover, slightly deviating from the social media framework, mobile phones and instant messaging activities have been frequently analyzed in [START_REF] Pozdnoukhov | Exploratory novelty identification in human activity data streams[END_REF][START_REF] Jo | Circadian pattern and burstiness in human communication activity[END_REF]. Despite their differences, all platforms unsurprisingly show a substantial decrease of activity during the night.

The realm of night owls is characterized not only by a general quiet but also by typical emotional markers. Emotional content of Twitter activity has been studied in several papers with different approaches [START_REF] Golder | Diurnal and seasonal mood vary with work, sleep, and daylength across diverse cultures[END_REF][START_REF] Dzogang | Circadian mood variations in Twitter content[END_REF][START_REF] Lampos | Analysing mood patterns in the United Kingdom through Twitter content[END_REF]. Despite the variety of data considered, all these papers share the same finding: digital nights are consistently characterized by a low level of shared emotions (both positive and negative).

Covid-19 lockdown partially disrupted these rhythms, by drastically changing people's habits and daily routines: from physical commuting to telecommuting, from school classes to distance learning, from in-person meetings to video calls. Within few days whole populations had to re-adapt their behaviors into a new life scenario characterized by deep health and professional concerns. Such unpredictable situation strongly impacted peoples' sleep-wake cycles, as reported in several studies based on surveys like [START_REF] Beck | The Coconel Group: Covid-19 health crisis and lockdown associated with high level of sleep complaints and hypnotic uptake at the population level[END_REF]. With our study, therefore, we create a link between the literature on circadian online rhythms and the one on the stress experienced by many societies in recent months.

Data and Methods

Since circadian patterns of online activity are strongly dependent on users' demography and on platforms' scope, as mentioned in the introduction, we conducted our study across two different platforms: YouTube and Twitter. This comparative framework will be central to distinguish platform-specific findings from more general trends.

The YouTube dataset

As mentioned in the introduction, the YouTube dataset is particularly interesting because of its temporal granularity. Indeed, historical data about the number of views can no longer be retrieve from the YouTube application programming interface (API), which only returns the views at the moment of querying and not their temporal evolution. Therefore, studies like the ones by [START_REF] Pinto | Using early view patterns to predict the popularity of YouTube videos[END_REF] and [START_REF] Nguyen | Analyzing and Predicting the Popularity of Online Contents[END_REF] involving time series of engagement metrics are not longer possible, unless constantly querying the API all along the period of interest, as we did.

The dataset covers 1031 popular French channels that (according to the experts we consulted) are particularly influential in the French public debate.

These channels, with their description, are listed in the Supplementary Material. The channels have been selected through a qualitative analysis of the French YouTube, aiming to identify a relevant actors that diffuse political opinions through the platform. The selected channels belong to the following categories: local and national media; influential Youtubers discussing political topics; militant associations; politicians; candidates for the European elections; political party; Yellow Vests groups; associations devoted to public causes; large public or private institutions. YouTube provides no information about the location from which videos are viewed, but since the channels of our corpus focus on French public debate, we can assume most of their viewers to be based in France. In collaboration with the Qatar Computing Research Institute (QCRI), we recorded hour by hour the evolution of views of each videos published after February 17, for an entire week after the publication. Between February 17 and April 14, we collected the views time series for 99.992 videos. For every video, we also collected the title, the description and other metadata available through the official YouTube API.

Before being able to perform our analysis, some preprocessing turned out to be necessary. Contrarily to what one might expect, the total number of views of a given video are not always increasing. Occasionally, YouTube removes from its counting earlier views that it deems to be fake because likely produced by bots, click-farming or through other illegitimate tricks, since YouTube wants "to make sure that videos are viewed by actual humans and not computer programs" [START_REF]Google: How engagement metrics are counted -YouTube Help[END_REF], as per the official support web-page. Since the corrections of these views are made after their recording, our dataset contain hours with a negative number of views. To correct such negative views, we have preprocessed our data in order to uniformly redistribute the corrections made at a given time on the previous hours. More precisely, if we call v h the views collected by a generic video at hour h after publication and T h the total number of views at hour h, if T h+1 < T h , we correct the time series as follows:

Tj = (1 -p) T j j = 1, . . . , h
where Tj is the corrected time series until hour h and p = T h -T h+1 T h is a percentage of correction.

The Twitter dataset

The Twitter dataset comprises about 8 millions tweets, retrieved through the official Twitter API, posted by 5161 active but non-professional users from February 17 to April 14. These non-professional users have been identified within a wider dataset of about 33 millions tweets containing Covid-19-related content. This corpus of tweets was collected by Science-Po MediaLab in Paris, by using the python based scraper Gazouilloire [START_REF]Gazouilloire[END_REF], a tool developed by Dime Web for systematic and configurable Twitter data collection through Twitter's official API. The data were collected based on a query of Covid-19-related words in French. All twitting and re-twitting times were collected in European Central Timezone (UTC +1). Being Covid-19 the most trending communication topic in France (as we can observe for example from Google Trends), since its first diffusion in Europe and even more around the lockdown decision, we can assume that a relevant part of the French Twittosphere is potentially present in this database.

Differently from the YouTube database, which does not allow extracting information on the users, for the Twitter database we can define precise profiles of the users we are interested to study, in order to have a more homogeneous, even if reduced, population. Since we are interested in the activity of common Twitter users, we decided to exclude newspapers, bloggers, radios, associations, etc. and only consider non-professional users. Moreover, recalling that the aim of this work is to provide robust cross-platform results, we needed the Twitter dataset to be comparable to the YouTube one: we hence had to restrict the content production on Twitter to the sole production taking place in France. The requirements listed above, together with the filtering they set off, can be clarified as follows:

• facing the need to exclude professional users, we only considered those [START_REF] Golder | Diurnal and seasonal mood vary with work, sleep, and daylength across diverse cultures[END_REF] whose profile did not contain keywords associated to professional use of the platform (e.g. "media", "blog", "official", etc.); ( 2) with a number of followers lower than the median of the whole dataset; (3) with an activity lower than the median activity (∼400 tweets by week);

• targeting a significant statistical analysis, we discarded users who published less than 100 tweets in the whole period;

• focusing on France, we filtered the sole users who explicitly declared their location to be in France, searching in the location descriptions multiple translations of "France", the name of all the cities in France with a population larger than 10000 inhabitants (with eventual translations), the French regions and departments.

This filtering left us with 5161 users: their Twitter profiles' descriptions have been manually checked to be sure that the non-professional selection mechanism was effective. Finally, in order to construct the dataset of tweets, the entire timelines of the selected users have been collected through the Twitter API, including tweets not related to Covid-19. Even though this sample is not meant to be representative of the full French Twittosphere, it provides a complete perspective of a sizable and homogeneous set of active non-professional users of the platform over the relevant time frame.

The tool for emotion and topic mining

To analyze the emotional and thematic contents of tweets and YouTube videos, we used a very well-known and tested tool: the LIWC dictionary [START_REF] Tausczik | The psychological meaning of words: LIWC and computerized text analysis methods[END_REF]. The LIWC dictionary classifies words on more than 70 emotional, stylistic and thematic dimensions and has been used in several analogous studies such as [START_REF] Golder | Diurnal and seasonal mood vary with work, sleep, and daylength across diverse cultures[END_REF][START_REF] Dzogang | Circadian mood variations in Twitter content[END_REF].

More precisely, the LIWC dictionary provides a list of words associated to each of the dimensions (for example, the category "Positive emotions" contains words like: happy, pretty, and good. Since the texts we analyze are written in French, we used the French version of the LIWC dictionary [START_REF] Piolat | La version française du dictionnaire pour le LIWC: modalités de construction et exemples d'utilisation[END_REF].

Results

The first major habit change generated by the 2020 spring lockdown in France is a considerable increase in the online activity. Recalling that the French first lockdown was announced on March 15 and enforced on the 17th, we can better understand the time series for Twitter posting, YouTube posting and YouTube views displayed in Fig. 1. All three time series show weekly and daily fluctuations. The average daily signals, smoothed by a moving average over a 7 day rolling window, reveal an increase of activity for Twitter posting and YouTube watching around the beginning of the lockdown. Notice that on both platforms the increase of activity started from the very moment the lockdown was announced (which itself sparked much debate).

As for the posting of videos on YouTube, such an activity is less casual and more stable than tweeting (particularly for the high-visibility channels that we monitored) and therefore conserved the same weekly and daily rhythms during the lockdown. Since the video production is hardly affected by the lockdown, we will not consider this dimension in the rest of the paper.

The rhythm of the night

To highlight the effects of the lockdown, in the following we analyze thematic and emotional changes before and after the start of the lockdown (March 17). We refer to the period before the lockdown as to the three weeks from February 17 to March 9. At the same time we will refer to the period after the lockdown enforcement as to the three weeks from March 23 to April 14. To exclude the transient effects of the transition phase, we discard the data about the two weeks around the lockdown onset (from the 9th to the 22nd of March). Preliminarly, we calculated the normalized daily activity profiles before and during lockdown for each hour of the day by

f Twitter (h) = d∈days N tweets (d, h) d∈days h∈{0,...,23} N tweets (d, h) (1)
and

f YouTube (h) = d∈days N views (h) d∈days h∈{0,...,23} N views (d, h), (2)
where h ∈ {0, . . . , 23} are the hours of day, d are the days considered, and N tweets (d, h) and N views (d, t) are respectively the number of tweets and of YouTube views at hour h of day d. The results are reported in the left plots of Fig. 2. We first observe that the profiles for Twitter and YouTube are quite different: while Twitter is mostly used during the day, with a strong activity decrease after midnight, YouTube is characterized by a higher night activity. While Twitter is an active media, characterized by a debating and prosuming culture [START_REF] Ritzer | The coming of age of the prosumer[END_REF] that encourages participation at the time of the day when engagement is maximum, videos watching on YouTube is, for many users, a more passive activity [START_REF] Khan | Social media engagement: What motivates user participation and consumption on youtube?[END_REF] which can easily fit the more relaxed late hours.

To quantify the differences between profiles before and during the lockdown, we calculated the relative differences of the normalized profiles:

δ(h) = f after (h) -f before (h) f after (h) + f before (h) (3)
This quantity is reported in the right plots of Fig. 2. Both YouTube and Twitter experienced an activity increase during the night and a smaller decrease of the activity in the early morning (6am-9am for Twitter and 9am-12am for YouTube). We observe that the morning decrease in Twitter is much smaller than the night increase. This suggests that, with the lockdown, people stayed longer awake during the night but without oversleeping in the morning.

To appraise the variations in the activity during lockdown nights, we compare this variation with another factor known to impact online circadian patterns: the weekly cycle of weekends and working days. We aggregate the data at the level of day and night: based on the shapes of the curves in Fig. 2, we consider night on Twitter the hours between 11PM and 6AM of the following day and on YouTube the hours between 1AM and 8AM. We decompose the aggregated activity into weekends and working days. To obtain comparable measures we divide the activity counts by the number of hours of the corresponding time period (night=7, day=17) and by the number of days of week parts (week-end=2, working days=5). The average number of tweets/views in the different categories are represented in Fig. 3, together with the relative changes among the classes. As we already observed, the night variations are the largest changes, both in weekends and working days. The activity increments due to lockdown are significantly larger than the variations associated with the normal the week cycle. In YouTube the variations also have opposite signs: while the activity normally decreases during weekend, it increases for lockdown. For both the platforms, and both for day and night, the most significant difference concerns the working days: the augmented social media usage seems to be replacing the time previously dedicated to daily routines (like commuting to work, going to sleep early, etc.) more than the time of recreational activities.

To confirm the hypothesis of reduced sleep during the lockdown, we analyze the situation at the individual level. For each Twitter user, we calculate the average time lag between two consecutive Tweets. Fig. 4 shows the hourly average of this measure colorred (and the boxplots to appreciate its variability) before and during the lockdown. While, in normal times, the average interevent times are much higher during the night (because of sleeping breaks), the lockdown flattened the curve, thereby suggesting a shortening of sleep intervals [START_REF] Beck | The Coconel Group: Covid-19 health crisis and lockdown associated with high level of sleep complaints and hypnotic uptake at the population level[END_REF]. In the right plot of Fig. 4 we display, for each hour of the night, the probability that the subsequent tweet is posted the following morning (between 7 AM and 12AM) rather than during the same night. This quantity represents the probability to "go to sleep" after an event at t 0 . For this analysis we only considered the inter-events that are longer than 1 hour, in order to get the last action only in a potential activity burst and reduce the noise. We also excluded all the inter-events finishing after the next morning. We see that, until 4AM, the probability to get asleep is lower during lockdown. These findings are based on an aggregated statistical study of the inter-events. Unfortunately, the short time span of our data collection (2 months) does not allow a more sophisticated analysis, for example, of the users chronotypes, which, as shown by [START_REF] Aledavood | Social network differences of chronotypes identified from mobile phone data[END_REF][START_REF] Aledavood | Daily rhythms in mobile telephone communication[END_REF] can be extremely important for understanding the individual sleep behavior.

What is night?

In this paragraph we analyze whether the quantitative changes observed in the previous paragraph correspond to differences in terms of contents. For Twitter, we build the sets K(d, h) containing all the hashtags posted in day d at hour h. For YouTube, we build the sets K(d, h) containing all the videos visualized in day d at hour h. We define the time similarity matrix, Θ, between two day's hours h 1 , h 2 , based on the Jaccard similarity between the sets K(d, h 1 ) and K(d, h 2 ) as:

Θ(h 1 , h 2 ) = 1 N days d∈days J(K(d, h 1 ), K(d, h 2 )) (4)
where

J(K(d, h 1 ), K(d, h 2 )) = |K(d,h1)∩K(d,h2)| |K(d,h1)∪K(d,h2
)| is the Jaccard similarity. Matrix Θ, represented in Fig. 5, indicates how the content shared or viewed at a certain hour is similar to the content in all the other hours. We perform a k-mean clustering procedure on this matrix to better identify the relationships between the hours of the day.

The results of the clustering are represented by the colors of the hours on the left of the plots of Fig. 5. Remarkably, these clusters identify different periods of the day, thereby showing that contents evolve along the day and different periods of the day are characterized by specific contents. Both for Twitter and YouTube, and both before and during lockdown, night hours (0am-5am) are characterized by contents distinctively different from the rest of the day. Before the lockdown, morning hours (6am-10am for Twitter and 6am-8am for YouTube) were the most different from night-time and constitute a well definite cluster. For Youtube before the lockdown, the late morning hours 9am-10am showed a return of the night contents. For both platforms before the lockdown, we observe a lunch-afternoon cluster and an evening cluster. Lockdown affected the morning cluster, though in opposite ways for the two platforms. In Twitter, the morning cluster extended to first hours of the afternoon cluster (lunch hours), while in YouTube the night vibe extended into the morning (until 11am). In Twitter, the lockdown shifted the afternoon cluster after lunch time (3pm-9pm) and consequently reduced the evening hours (10pm-11pm). In YouTube, we observe the emergence of contents dedicated to the lunch hours (12am-2pm) and a second uniform block until covering the afternoon and the evening (3pm-11pm).

A significant change of content

We proceed with the analyses of the emotional and thematic content of Twitter and YouTube activities, before and during the lockdown. Using the categories of the LIWC dictionary we will consider three separated analytic dimensions:

• General Affects: Positive Affect, Negative Affect;

• Specific Emotions: Sadness, Anger, Anxiety and Accomplishment:

• Thematic contents: Work, Social life, Religion, Death, Fun, Exclusion, Biology, Money.

We first assign the tweets and YouTube videos (based on the words contained in their titles and descriptions) to one category for each dimension. To do so, we count how many terms from each category are contained in each tweet/video, and we assign the content to the prevalent category. For example, for the dimension "General Affect" each content is categorized as either Positive or Negative Affect or not classified if the items contains no categorical words or similar proportions of positive and negative terms. We also consider the global emotional level ("Affect") of the items, by counting together the positive and negative words. For each dimension, we compute the fraction of tweets and retweets in each category during the lockdown and the difference compared to the previous period. In the same way, for YouTube, we evaluate the fraction of visualization of videos in each category over the total number of views. The results are reported in the left plot of Fig. 6.

Comparing the two platforms, we first observe that YouTube is more "emotional" than Twitter and is generally populated by more positive content. Both platforms experience a decrease of the emotional sphere during the lockdown, but on YouTube in particular we observe an increase of emotionally negative contents. Regarding specific emotions, we notice that expressions of accomplishment decline in both platforms. Instead, while Twitter experienced a decrease of all specific emotions, YouTube, which was already characterized by a higher level of anger, sadness and anxiety before the lockdown, goes through an important increase of these sentiments. From a thematic point of view we observe, unsurprisingly, a decrease of the contents related to social life and leisure and an increase of contents related to death and house. On Twitter we also have a significant increase of religion-related contents. All differences in distribution of contents before and during the lockdown have been tested statistically with Kolmogorov-Smirnov (KS) tests. For both platforms before and during the lockdown an hourly aggregation has been performed in order to get two different samples of emotion distribution. The results of the KS test over those distributions are reported in Table 1 andTable 2. and most of the times support the statistical relevance of differences in content distribution before and during the lockdown.

2.4 Because the night belongs to...

Drawing on our previous hour clustering, we divide the day according to five time periods

: [0am-5am],[6am-9am],[10am-2pm],[3pm-6pm],[7pm-12pm
] to identify a circadian profile for each of our categories (right plot of Fig. 6). For several categories related to emotions, we can first notice an interesting Twitter/YouTube difference: what peaks in the early morning on Twitter [6am-9am] tends to peak in the following interval in YouTube [10am-2pm], thereby suggesting that YouTube content is consumed later in the day. Going into more detail, in agreement with the findings of [START_REF] Golder | Diurnal and seasonal mood vary with work, sleep, and daylength across diverse cultures[END_REF][START_REF] Dzogang | Circadian mood variations in Twitter content[END_REF][START_REF] Lampos | Analysing mood patterns in the United Kingdom through Twitter content[END_REF] we observe that nights are characterized by low emotional levels, especially positive ones, while both positivity and negativity tend to peak at the moment of the awakening. This pattern is more evident on Twitter also at the level of specific emotions, while on YouTube a significant portion of negative contents is consumed during the night.

An interesting observation, again in phase with the precedent findings of [START_REF] Golder | Diurnal and seasonal mood vary with work, sleep, and daylength across diverse cultures[END_REF][START_REF] Dzogang | Circadian mood variations in Twitter content[END_REF][START_REF] Lampos | Analysing mood patterns in the United Kingdom through Twitter content[END_REF], is that the daily emotional patterns seem to be resilient to the Covid-19 disruption: even if the volumes of some emotions changed during the lockdown, their daily distribution generally maintained the same shape, as demonstrated by a rough parallelism of the lines before and during the lockdown (with some exceptions regarding anger and anxiety on YouTube). This fact confirms the observation made in [START_REF] Golder | Diurnal and seasonal mood vary with work, sleep, and daylength across diverse cultures[END_REF] that external factors, even as important as the Covid-19 lockdown, influence the emotional patterns less than the sleep-wake cycles. Interestingly, this is not the case for the distribution of topics which has been more significantly influenced by the lockdown.

Discussion

The Covid-19 pandemic and the ensuing lockdown have deeply and widely disrupted people's daily routines. Our research exposed some of these changes through the lens of social media. By highlighting what has changed during the lockdown and what has resisted the Covid-19 shock, our research proves that certain online habits are more resilient to external disruption than others, thereby suggesting which human behaviors are more influenced by exogenous factors and which are, on the contrary, constant even in exceptional situations.

Circadian rhythms of activity proved to be strongly related to lifestyle and working hours: the change observed in the lockdown rhythms suggests in particular that in the absence of external constraints such as school and office hours, the boundaries between night and day become more flexible.

Perhaps surprisingly, we found out that the emotional charge of tweets and YouTube videos decreased with the lockdown, arguably leaving space to less emotional contents. However, this general finding is tempered by the fact that on YouTube (which is inherently a more emotional medium than Twitter) negative sentiments like anger and anxiety did increase, thus revealing the stressful situation for the population. As topics are concerned, online discussions proved to follow real world events and, unsurprisingly in a global epidemic that forced people at home, shifted towards questions connected to biology, house, and death.

As an even more interesting result, we pointed out the resilience of emotional patterns in online activities. While the general emotional charge of online contents decreased during the lockdown, it maintained its normal daily distribution. After March 17th, nightlife continues to be characterized by less emotional content despite the stress caused by the Covid-19 crisis. Even if the circadian rhythms change and people stay awake longer, at night, they seem to continue to share and consume the same type of contents.

In future research, we would like to investigate more in depth the nature of this low-emotional nighttime space, in order to reveal weather it consists of more informative and impartial contents and it gives rise to positive and constructive forms of debate or, on the contrary, whether it is more markedly affected by fake news and other types of misinformation. The LIWC dictionary used so far allowed us to distinguish emotional from unemotional contents: more specific dictionaries could lead to deeper insights about nighttime activity and to better understand the relationship between information and emotion in different medias. Broadly speaking, we hope that noticing the resilience of some online patterns during the lockdown might encourage future research in emotional rhythms and their reaction to external shocks.

Before concluding, we would like to briefly discuss two limitations of our study. In this research, we analyzed two different platforms, therefore providing insights on two different types of public . However, we should remind that these two viewpoints are not sufficient to completely represent the French social media and, even less, French society. A comparison with other type of data, not available to our team, like phone call datasets or mobile usage information would be useful to confirm and refine our findings. As a second limitation, our analysis is limited to a single country and on the period of the first lockdown. The continued and worldwide impact of the Covid-19 crisis call for a comparison with similar analyses in other countries and in other phases of the pandemics.

Tables Table 1: p-values of Kolmogorov-Smirnov tests for YouTube content differences displayed by Fig. 6,i

Figures

  Figures

Figure 1 :Figure 2 :Figure 5 :

 125 Figure 1: Increase of platforms activity after the lockdown. (top) Evolution of number of visualizations by day on YouTube. (middle) Evolution of number of new published videos on YouTube. (bottom) Evolution of number of Covid-19 related tweets or re-tweets

Figure 6 :

 6 Figure 6: Themes and Emotions before and during lock-down. Left plot: Fraction of videos/Tweets with a content and relative change with lockdown. The size of the points is proportional to the fractions (quantified by the upper numbers). The orientation of the line indicates if there was an increase (orientation toward right) or decrease (toward left) with the lockdown. The length of the line is proportional to the percentage increase/decrease with the lockdown. Right plot: Fraction of videos/Tweets with a content by hour. The continuous line indicates the fractions after the lockdown, the dotted lines before. An arrow starts from the before to the after line for each hour period: if the arrow is oriented towards the top, the lockdown increased the content fraction in the selected hours and viceversa. In both plots YouTube is in red, Twitter is in blue. 20

  .e. content differences before and during the lockdown

	Category	Avg Before Lockdown	Avg During Lockdown	KS p-value
	Negative Affect	0.187	0.202	2.29 • 10 -9
	Positive Affect	0.693	0.647	∼ 0
	Affect	0.961	0.938	∼ 0
	Sadness	0.118	0.127	7.56 • 10 -8
	Anger	5.17 • 10 -2	5.78 • 10 -2	3.16 • 10 -12
	Anxiety	2.15 • 10 -2	2.88 • 10 -2	2.31 • 10 -7
	Accomplishment 0.575	0.571	0.075
	Work	0.278	0.285	0.0025
	Social Life	0.419	0.341	∼ 0
	Religion	1.91 • 10 -3	1.67 • 10 -3	1.29 • 10 -4
	Death	1.96 • 10 -3	5.64 • 10 -3	∼ 0
	Leisure	3.95 • 10 -2	3.77 • 10 -2	1.52 • 10 -10
	Exclusion	2.35 • 10 -2	2.85 • 10 -2	1.82 • 10 -14
	Biology	9.70 • 10 -2	0.14	∼ 0
	Money	0.109	0.123	2.22 • 10 -16

Table 2

 2

	: p-values of Kolmogorov-Smirnov tests for Twitter content differences
	displayed by Fig. 6, i.e. content differences before and during the lockdown
	Category	Avg Before Lockdown	Avg During Lockdown	KS p-value
	Negative Affect	0.275	0.261	3.11 • 10 -15
	Positive Affect	0.268	0.256	3.11 • 10 -15
	Affect	0.659	0.628	3.11 • 10 -15
	Sadness	5.55 • 10 -2	5.54 • 10 -2	0.984
	Anger	3.92 • 10 -2	3.50 • 10 -2	3.11 • 10 -12
	Anxiety	1.15 • 10 -2	9.39 • 10 -3	3.11 • 10 -12
	Accomplishment 1.46 • 10 -1	1.32 • 10 -1	3.11 • 10 -12
	Work	6.96 • 10-2 5.58 • 10-2	0.0025
	Social Life	0.119	0.117	1.46 • 10 -6
	Religion	6.87 • 10 -3	7.14 • 10 -3	3.85 • 10 -3
	Death	5.51 • 10 -3	5.90 • 10 -3	1.03 • 10 -3
	Leisure	5.34 • 10 -2	4.57 • 10 -2	3.11 • 10 -15
	Exclusion	1.37 • 10 -1	1.34 • 10 -1	1.73 • 10 -8
	Biology	1.06 • 10 -1	1.03 • 10 -1	4.20 • 10 -8
	Money	5.91 • 10 -2	4.51 • 10 -2	3.11 • 10 -15

Acknowledgments

F.G. thanks Jeremy Ward for the useful discussions. A note of thanks and major acknowledgment goes to Yoan Dinkov and Preslav Nakov of the Qatar Computing Research Institute (QCRI) for their help in collecting YouTube data. A special thanks goes to Bilel Benbouzid for the precious discussions on the French YouTube landscape.

Funding

This research has been supported by the French national science foundation (Agence Nationale de la Recherche) through project TRACTRUST and by CNRS through the 80 PRIME MITI project "Disorders of Online Media" (DOOM).

Availability of data and material

Authors agree to make their data available upon request. The list of the YouTube channels is reported in the Supplementary Material.

Competing interests

The authors declare that they have no competing interests.

Author's contributions M.C. and F.G. collected the missing data and analyzed the data. All authors conceived the research, discussed the results and wrote the manuscript. Probability that a tweet following a tweet at t 0 is posted on the following morning (dashed=before lockdown, solid=during lockdown).