Peer review of: Synchronization of complex human networks (2020)

REVIEWER COMMENTS

Reviewer #1 (Remarks to the Author): 

This paper presents a careful and well-thought-out experiment and analysis of humans attempting to 
synchronize their individually periodic behavior --- in this case, violinists cyclically repeating an 
assigned musical phrase. A very striking general result is the extent to which this human activity is 
shown to yield distinct kinds of activity reminiscent of behaviors of physical and biological systems of 
much greater simplicity. Transitions between these distinct kinds of behavior ("dynamical phase 
transitions") are cleanly demonstrated and explained. Moreover, the paper presents an innovative 
experimental implementation and study of the effects of network structure and time delay along links. 
One of the more striking results is the discovery of a phenomenon whereby, under appropriate 
circumstances, a human effectively breaks a communication link from one of its neighbors in order to 
maintain sync with another neighbor. This work will be of great general interest as a paradigm for the 
study of synchronized behavior of groups of humans and of other complex systems. 
The authors may be interested in citing the following additional reference: E. Ott and T.M. Antonsen, 
Jr., "Frequency and Phase Synchronism in Large Groups: Low Dimensional Description of 
Synchronized Clapping, Firefly Flashing, and Cricket Chirping," CHAOS, vol.27, 051101 {2017). 



Reviewer #2 (Remarks to the Author): 

I found the experiments and results to be moderately interesting, especially the adaptions that 
humans make to maintain synchronization under challenging conditions. I say only “moderately” 
because the task itself (repeatedly playing a single musical phrase) is so contrived and artificial; 
consequently, it’s unclear how far the results will generalize, but still, this is a useful and original study 
of human rhythmic synchronization and its dependence on delay and coupling patterns. It’s also 
notable that the authors found a generalization of the Kuramoto model that could account for the main 
results. The claim that the precise mechanism for ignoring frustrating interactions did not matter (any 
of three mechanisms will do) was surprising and interesting. I can well imagine this paper stimulating 
further work, both experimentally and theoretically, so I would recommend publication. 

Two suggestions: 

1) In the schematic diagrams of the network structures (Figures 3-7), I could not make sense of the 
arrows along the edges between players. What does a single directed arrow mean? Or a bidirectional 
double arrow? Does an arrow pointing from player a to player b mean that player a is phase-leading 
player b (and if so, by what amount of phase difference, or is that irrelevant to the arrow notation)? In 
any case, the arrow notation needs to be explained in the main text and in the figure captions. 

2) In the introduction, the authors write, “To date, there are no studies of the synchronization of 
complex human networks”. This seems a bit of an overstatement. The claim is perhaps defensible if 
synchronization is taken in a narrow sense to mean synchronization of *rhythmic* behavior. But 
synchronization in the broader sense of consensus and coordination has been studied experimentally 
by Michael Kearns and collaborators for human decision-making tasks on complex networks, e.g., 

Behavioral dynamics and influence in networked coloring and consensus 
Stephen Judd, Michael Kearns, Yevgeniy Vorobeychik 
Proceedings of the National Academy of Sciences Aug 2010, 107 (34) 14978-14982; DOI: 
10.1073/pnas.1001280107 
An Experimental Study of the Coloring Problem on Human Subject Networks, by Michael Kearns, 
Siddharth Suri, and Nick Montfort, Science 11 Aug 2006: Vol. 313, Issue 5788, pp. 824-827 
DOI: 10.1126/science.1127207 

In a related vein, there are potentially relevant studies on the “wisdom of the crowd” under different 
network conditions, in work by Damon Centola and others, e.g., 

Network dynamics of social influence in the wisdom of crowds 
Joshua Becker, Devon Brackbill, and Damon Centola 
PNAS June 27, 2017 114 (26) E5070-E5076 



Reviewer #3 (Remarks to the Author): 

This paper presents an interesting experimental study of synchronization in a human network of 
interacting violin players. I had reviewed an early version of this paper. The following points remain to 
be addressed before a publication recommendation can be made. 

1. Why is the playing period of each player T_i(t) a function of time? How is it measured exactly? 

2. It would be better to introduce an equation to define the coupling strength. What does it mean "... 
and according to a logarithmic scale"? 

3. Often the terminology used is not explained as for the cases of "crowd synchrony" or "out-of-phase 
synchronization". One cannot expect the broad readership of NC to be familiar with technical terms 
like these. The other major problem is that complex concepts such as "vortex synchronization" or 
"arrowhead synchronization" are introduced by looking at figures. I suggest that these states are first 
defined and then illustrated in figures. 

4. The experiment about increasing the communication delay is interesting. However, I have the 
following questions: "the players are able to perceive an increase of the communication delay while 
they are playing. Correct? So they may be able to figure what the actual delay is as time progresses. 
If yes, then I would argue a control experiment is needed in which the delay is static and does not 
change in time. 

5. One of the main findings is the emergence of an effective network coupling topology for which 
certain links are neglected/ignored. However this could be better explained. 
How is the effective topology determined? Is it time invariant? Are the connections of this topology 
always bidirectional? Also, it appears some of these preferred emerging topology are "square motifs or 
open chains" -- is there an explanation for this? An alternative counter-explanation for neglecting 
some of the links, which would find excellent analogies in the studies on coordinated motion of 
animals, is that the human/animal mind can only keep track of a limited number of "signals" at the 
same time. 
6. " Therefore, the speciﬁc psychology of each player has no role in the macroscopic network 
dynamics of coupled violin players" not sure psychology is the right word here? 

7. It's good that the paper presents a simple model that attempts to explain the experimental 
observations. However, I do not understand how in the model the three different mechanisms 
considered for deleting links can all lead to the same dynamics. Do the authors have a clear 
understanding of this? Also, how are the frequencies of the Kuramoto oscillators and all the 
parameters (eg coupling strengths, eta, etc) chosen? An alternative model could include a mechanism 
for network adaptation in which the coupling strengths are tuned in order to maintain synchronization, 
see Physical Review E 79 (1), 016201 2009 and CHAOS 20 (1), 013103 2010. 

8. What do the authors exactly mean by "adjust the periodicity"? 

9. This sentence from the conclusions is a bit vague: " Our system will be extended to investigate 
decision making models in different conﬁgurations, bifurcation and phase transition in human 
networks, and the nonlinearity of crowds. "