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Statistical mechanics of steiner trees.
TLDR
A general technique to translate the imposed global connectivity constrain into many local ones that can be analyzed with cavity equation techniques leads to a new optimization algorithm for MST and allows to analyze the statistical mechanics properties of MST on random graphs of various types.
Entropy landscape and non-Gibbs solutions in constraint satisfaction problems
TLDR
It is shown that a smoothed version of a decimation strategy based on belief propagation is able to find solutions belonging to subdominant clusters even beyond the so-called rigidity transition where the thermodynamically relevant clusters become frozen.
Statistical mechanics of maximal independent sets.
TLDR
This paper uses cavity method of statistical physics and Monte Carlo simulations to study the corresponding constraint satisfaction problem on random graphs, and obtains the entropy of maximal independent sets within the replica symmetric and one-step replica symmetry breaking frameworks.
Statistical physics approach to graphical games: local and global interactions
TLDR
A representation of games that extends over graphical games to deal conveniently with both local a global interactions and the cavity method of statistical physics to study the geometrical structure of the equilibria space is considered.
Investigation of a protein complex network
TLDR
It is found that the network of protein complexes in the budding yeast Saccharomyces cerevisiae is a small world network with scale free behavior for many of its distributions, but there are no strong correlations between the weights and degrees of neighboring complexes.
Stochastic matching problem.
TLDR
This work proposes an efficient method to solve stochastic matching problems which combines some features of the survey propagation equations and of the cavity method and is shown numerically to be effective on the full range of parameters, and to outperform state-of-the-art methods.
Circuit topology of linear polymers: a statistical mechanical treatment
TLDR
This work studies circuit topology landscapes of linear polymer chains with intra-chain contacts as a prototype of linearly sorted objects with interactions to find generic features of the topological space and study the statistical properties of the space under the most basic constraints on the occupancy of arrangements and topological interactions.
Inference and learning in sparse systems with multiple states.
TLDR
This work takes as a model system the finite connectivity Hopfield model in the memory phase and suggests a cavity method approach to reconstruct the couplings when the data are separately sampled from few attractor states.
Simple models of small-world networks with directed links.
TLDR
The interplay of shortcuts and unfavorable bonds on the small world properties is studied and a quantity identified as the average size of the accessible world in the model is defined.
Generating correlated networks from uncorrelated ones.
TLDR
It is shown that the transformation which converts these graphs to their line (edge-dual) graphs produces an ensemble of graphs with nearly the same degree distribution, but with degree correlations and a much higher clustering coefficient.
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