Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kac-Rice formulas and the number of solutions of parametrized systems of
  polynomial equations   Kac-Rice formulas express the expected number of elements a fiber of a random
field has in terms of a multivariate integral. We consider here parametrized
systems of polynomial equations that are linear in enough parameters, and
provide a Kac-Rice formula for the expected number of solutions of the system
when the parameters follow continuous distributions. Combined with Monte Carlo
integration, we apply the formula to partition the parameter region according
to the number of solutions or find a region in parameter space where the system
has the maximal number of solutions. The motivation stems from the study of
steady states of chemical reaction networks and gives new tools for the open
problem of identifying the parameter region where the network has at least two
positive steady states. We illustrate with numerous examples that our approach
successfully handles a larger number of parameters than exact methods.

19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom