Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiscale dynamical embeddings of complex networks   Complex systems and relational data are often abstracted as dynamical
processes on networks. To understand, predict and control their behavior, a
crucial step is to extract reduced descriptions of such networks. Inspired by
notions from Control Theory, we propose a time-dependent dynamical similarity
measure between nodes, which quantifies the effect a node-input has on the
network. This dynamical similarity induces an embedding that can be employed
for several analysis tasks. Here we focus on (i)~dimensionality reduction,
i.e., projecting nodes onto a low dimensional space that captures dynamic
similarity at different time scales, and (ii)~how to exploit our embeddings to
uncover functional modules. We exemplify our ideas through case studies
focusing on directed networks without strong connectivity, and signed networks.
We further highlight how certain ideas from community detection can be
generalized and linked to Control Theory, by using the here developed dynamical
perspective.

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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
2
The categories of this paper are: math
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The categories of this paper are: nlin
10
The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat