Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting solutions from finite samplings   We formulate the solution counting problem within the framework of inverse
Ising problem and use fast belief propagation equations to estimate the entropy
whose value provides an estimate on the true one. We test this idea on both
diluted models (random 2-SAT and 3-SAT problems) and fully-connected model
(binary perceptron), and show that when the constraint density is small, this
estimate can be very close to the true value. The information stored by the
salamander retina under the natural movie stimuli can also be estimated and our
result is consistent with that obtained by Monte Carlo method. Of particular
significance is sizes of other metastable states for this real neuronal network
are predicted.

10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys