Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relationships between the Distribution of Watanabe-Strogatz Variables
  and Circular Cumulants for Ensembles of Phase Elements   The Watanabe-Strogatz and Ott-Antonsen theories provided a seminal framework
for rigorous and comprehensive studies of collective phenomena in a broad class
of paradigmatic models for ensembles of coupled oscillators. Recently, a
"circular cumulant" approach was suggested for constructing the perturbation
theory for the Ott-Antonsen approach. In this paper, we derive the relations
between the distribution of Watanabe-Strogatz phases and the circular cumulants
of the original phases. These relations are important for the interpretation of
the circular cumulant approach in the context of the Watanabe-Strogatz and
Ott-Antonsen theories. Special attention is paid to the case of hierarchy of
circular cumulants, which is generally relevant for constructing perturbation
theories for the Watanabe-Strogatz and Ott-Antonsen approaches.

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The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
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The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th