Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Note on Local Mode-in-State Participation Factors for Nonlinear
  Systems   The paper studies an extension to nonlinear systems of a recently proposed
approach to the concept of modal participation factors. First, a definition is
given for local mode-in-state participation factors for smooth nonlinear
autonomous systems. The definition is general, and, unlike in the more
traditional approach, the resulting participation measures depend on the
assumed uncertainty law governing the system initial condition. The work
follows Hashlamoun, Hassouneh and Abed (2009) in taking a mathematical
expectation (or set-theoretic average) of a modal contribution measure with
respect to an assumed uncertain initial state. As in the linear case, it is
found that a symmetry assumption on the distribution of the initial state
results in a tractable calculation and an explicit and simple formula for
mode-in-state participation factors.

15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con