Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Synchronization conditions in the Kuramoto model and their relationship
  to seminorms   In this paper we address two questions about the synchronization of coupled
oscillators in the Kuramoto model with all-to-all coupling. In the first part
we use some classical results in convex geometry to prove bounds on the size of
the frequency set supporting the existence of stable, phase locked solutions
and show that the set of such frequencies can be expressed by a seminorm which
we call the Kuramoto norm. In the second part we use some ideas from extreme
order statistics to compute upper and lower bounds on the probability of
synchronization for very general frequency distributions. We do so by computing
exactly the limiting extreme value distribution of a quantity that is
equivalent to the Kuramoto norm.

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The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex