Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Collective frequency variation in network synchronization and reverse
  PageRank   A wide range of natural and engineered phenomena rely on large networks of
interacting units to reach a dynamical consensus state where the system
collectively operates. Here we study the dynamics of self-organizing systems
and show that for generic directed networks the collective frequency of the
ensemble is {\it not} the same as the mean of the individuals' natural
frequencies. Specifically, we show that the collective frequency equals a
weighted average of the natural frequencies, where the weights are given by an
out-flow centrality measure that is equivalent to a reverse PageRank
centrality. Our findings uncover an intricate dependence of the collective
frequency on both the structural directedness and dynamical heterogeneity of
the network, and also reveal an unexplored connection between synchronization
and PageRank, which opens the possibility of applying PageRank optimization to
synchronization. Finally, we demonstrate the presence of collective frequency
variation in real-world networks by considering the UK and Scandinavian power
grids.

22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int