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**1 - 2**of**2**### Efficient Monte Carlo Methods for the Potts Model at Low Temperature

, 2015

"... We consider the problem of estimating the partition function of the ferromagnetic q-state Potts model. We propose an importance sampling algorithm in the dual of the normal factor graph representing the model. The algorithm can efficiently compute an estimate of the partition function when the coup ..."

Abstract
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We consider the problem of estimating the partition function of the ferromagnetic q-state Potts model. We propose an importance sampling algorithm in the dual of the normal factor graph representing the model. The algorithm can efficiently compute an estimate of the partition function when the coupling parameters of the model are strong (corresponding to models at low temperature) or when the model contains a mixture of strong and weak couplings. We show that, in this setting, the proposed algorithm significantly outperforms the state of the art methods.

### Convex inference for community discovery in signed networks ∗

"... In contrast to traditional social networks, signed ones encode both relations of affinity and disagreement. Community discovery in this kind of networks has been successfully addressed using the Potts model, originated in statistical me-chanics to explain the magnetic dipole moments of atomic spins. ..."

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In contrast to traditional social networks, signed ones encode both relations of affinity and disagreement. Community discovery in this kind of networks has been successfully addressed using the Potts model, originated in statistical me-chanics to explain the magnetic dipole moments of atomic spins. However, due to the computational complexity of finding an exact solution, it has not been ap-plied to many real-world networks yet. We propose a novel approach to compute an approximated solution to the Potts model applied to the context of community discovering, which is based on a continuous convex relaxation of the original prob-lem using hinge-loss functions. We show empirically the benefits of the proposed method in comparison with loopy belief propagation in terms of the communities discovered. We illustrate the scalability and effectiveness of our approach by ap-plying it to the network of voters of the European Parliament that we have crawled for this study. This large-scale and dense network comprises about 300 votings pe-riods on the actual term involving a total of more than 730 voters. Remarkably, the two major communities are those created by the european-antieuropean antag-onism, rather than the classical right-left antagonism. 1