Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A complexity dichotomy for partition functions with mixed signs   Partition functions, also known as homomorphism functions, form a rich family
of graph invariants that contain combinatorial invariants such as the number of
k-colourings or the number of independent sets of a graph and also the
partition functions of certain "spin glass" models of statistical physics such
as the Ising model.
  Building on earlier work by Dyer, Greenhill and Bulatov, Grohe, we completely
classify the computational complexity of partition functions. Our main result
is a dichotomy theorem stating that every partition function is either
computable in polynomial time or #P-complete. Partition functions are described
by symmetric matrices with real entries, and we prove that it is decidable in
polynomial time in terms of the matrix whether a given partition function is in
polynomial time or #P-complete.
  While in general it is very complicated to give an explicit algebraic or
combinatorial description of the tractable cases, for partition functions
described by a Hadamard matrices -- these turn out to be central in our proofs
-- we obtain a simple algebraic tractability criterion, which says that the
tractable cases are those "representable" by a quadratic polynomial over the
field GF(2).

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The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: eess
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: math-ph