# Computing loop corrections by message passing

@article{Ramezanpour2013ComputingLC, title={Computing loop corrections by message passing}, author={Abolfazl Ramezanpour}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2013}, volume={87 6}, pages={ 060103 } }

Any spanning tree in a loopy interaction graph can be used for communicating the effect of the loopy interactions by introducing messages that are passed along the edges in the spanning tree. This defines an exact mapping of the problem on the loopy interaction graph onto an extended problem on a tree interaction graph, where the thermodynamic quantities can be computed by a message-passing algorithm based on the Bethe equations. We propose an approximation loop correction algorithm for the…

## 3 Citations

Statistical physics of loopy interactions: Independent-loop approximation and beyond

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

This work considers an interacting system of spin variables on a loopy interaction graph, identified by a tree graph and a set of loopy interactions, and finds the sum over the loop configurations can be computed "exactly" by the belief propagation algorithm in the low orders of the approximation as long as the loops have a tree structure.

Cycle-Based Cluster Variational Method for Direct and Inverse Inference

- Mathematics, Computer Science
- 2016

This work addresses both the direct and inverse problem with mean-field methods of statistical physics, going beyond the Bethe approximation and associated belief propagation algorithm, and proposes two complementary methods based respectively on fixed point equations and on a one-parameter log likelihood function minimization.

Distance measures and evolution of polymer chains in their topological space.

- BiologySoft matter
- 2015

This study provides a first theoretical framework for topological transition, i.e. conformational transitions that are associated with changes in molecular topology, and presents an algorithm for estimating the number of intermediate topologies visited during a topological reaction.

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