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Dynamics of the Belief Propagation for the Ising Model

100%
Siudem G., Świątek G.
Acta Physica Polonica A
|
2015
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vol. 127
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issue 3A
A-145-A-149
EN
The Belief Propagation algorithm is a popular technique of solving inference problems for different graph-like structures. We present a discussion of the dynamics of that algorithm for the Ising model on the square lattice. Our main goal was to describe limit fixed points for that algorithm, which are strictly connected with the marginal probabilities and stationary points of the Bethe Free Energy. Analytical considerations provide an exact analysis of a class of symmetrical points while numerical simulations confirm that for small lattices there are no non-symmetrical points. Notwithstanding the prevalent use of the Belief Propagation as an inference tool we present a sociophysical interpretation of its dynamics. In that case our considerations may be viewed as an investigation of the possible fixed points of the social dynamics.
2
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Majority Vote Model on Multiplex Networks

81%
Krawiecki A., Gradowski T., Siudem G.
Acta Physica Polonica A
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2018
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vol. 133
|
issue 6
1433-1440
EN
Majority vote model on multiplex networks with two independently generated layers in the form of scale-free networks is investigated by means of Monte Carlo simulations and heterogeneous mean-field approximation. In a version of the model under study each agent with probability 1-q (0≤q≤1/2) follows the opinions of the majorities of her neighbors within both layers if these opinions are identical; otherwise, she makes decision randomly. The model exhibits second-order ferromagnetic transition as q, the parameter measuring the level of internal noise, is decreased, with critical exponents depending on the details of the degree distributions in the layers. The critical value q_{c} of the parameter q evaluated in the heterogeneous mean-field approximation shows quantitative agreement with that obtained from numerical simulations for a broad range of parameters characterizing the degree distributions of the layers.
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