Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enumerating contingency tables via random permanents   Given m positive integers R=(r_i), n positive integers C=(c_j) such that sum
r_i = sum c_j =N, and mn non-negative weights W=(w_{ij}), we consider the total
weight T=T(R, C; W) of non-negative integer matrices (contingency tables)
D=(d_{ij}) with the row sums r_i, column sums c_j, and the weight of D equal to
prod w_{ij}^{d_{ij}}. We present a randomized algorithm of a polynomial in N
complexity which computes a number T'=T'(R,C; W) such that T' < T < alpha(R, C)
T' where alpha(R,C) = min{prod r_i! r_i^{-r_i}, prod c_j! c_j^{-c_j}} N^N/N!.
In many cases, ln T' provides an asymptotically accurate estimate of ln T. The
idea of the algorithm is to express T as the expectation of the permanent of an
N x N random matrix with exponentially distributed entries and approximate the
expectation by the integral T' of an efficiently computable log-concave
function on R^{mn}. Applications to counting integer flows in graphs are also
discussed.

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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: stat
37
The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph