Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantifying Transient Spreading Dynamics on Networks   Spreading phenomena on networks are essential for the collective dynamics of
various natural and technological systems, from information spreading in gene
regulatory networks to neural circuits or from epidemics to supply networks
experiencing perturbations. Still, how local disturbances spread across
networks is not yet quantitatively understood. Here we analyze generic
spreading dynamics in deterministic network dynamical systems close to a given
operating point. Standard dynamical systems' theory does not explicitly provide
measures for arrival times and amplitudes of a transient, spreading signal
because it focuses on invariant sets, invariant measures and other quantities
less relevant for transient behavior. We here change the perspective and
introduce effective expectation values for deterministic dynamics to work out a
theory explicitly quantifying when and how strongly a perturbation initiated at
one unit of a network impacts any other. The theory provides explicit timing
and amplitude information as a function of the relative position of initially
perturbed and responding unit as well as on the entire network topology.

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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an