Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Euclidean distance degree and mixed volume   We initiate a study of the Euclidean Distance Degree in the context of sparse
polynomials. Specifically, we consider a hypersurface f=0 defined by a
polynomial f that is general given its support, such that the support contains
the origin. We show that the Euclidean Distance Degree of f=0 equals the mixed
volume of the Newton polytopes of the associated Lagrange multiplier equations.
We discuss the implication of our result for computational complexity and give
a formula for the Euclidean distance degree when the Newton polytope is a
rectangular parallelepiped.

23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn