Efficient and Convergent Preconditioned ADMM for the Potts Models

2021 ◽  
Vol 43 (2) ◽  
pp. B455-B478
Author(s):  
Hongpeng Sun ◽  
Xue-Cheng Tai ◽  
Jing Yuan
Keyword(s):  
Potts Models

Large q expansions for q-state gauge-matter Potts models in lagrangian form

1980 ◽  
Vol 170 (3) ◽  
pp. 409-432 ◽  
Author(s):  
Paul Ginsparg ◽  
Yadin Y. Goldschmidt ◽  
Jean-Bernard Zuber
Keyword(s):  
Potts Models ◽  
Lagrangian Form

scholarly journals Phase Transitions of Ferromagnetic Potts Models on the Simple Cubic Lattice

2014 ◽  
Vol 31 (7) ◽  
pp. 070503 ◽  
Author(s):  
Shun Wang ◽  
Zhi-Yuan Xie ◽  
Jing Chen ◽  
Bruce Normand ◽  
Tao Xiang
Keyword(s):  
Phase Transitions ◽  
Potts Models ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice

scholarly journals Geometric and stochastic clusters of gravitating Potts models

2006 ◽  
Vol 639 (3-4) ◽  
pp. 373-377 ◽  
Author(s):  
Wolfhard Janke ◽  
Martin Weigel
Keyword(s):  
Potts Models

scholarly journals A study on critical universality of the random-bond Potts models with self-dual quenched randomness

2004 ◽  
Vol 53 (1) ◽  
pp. 265
Author(s):  
Ren Hao ◽  
Gu De-Wei ◽  
Pan Zheng-Quan ◽  
Ying He-Ping
Keyword(s):  
Potts Models ◽  
Quenched Randomness

scholarly journals PPalign: Optimal alignment of Potts models representing proteins with direct coupling information

2020 ◽  
Author(s):  
Hugo Talibart ◽  
François Coste
Keyword(s):  
Markov Models ◽  
Pairwise Alignment ◽  
Homology Search ◽  
Sequence Alignments ◽  
Potts Models ◽  
Functional Annotations ◽  
Current State ◽  
Linear Programming Formulation ◽  
Computational Bottleneck ◽  
New Research

AbstractBackgroundTo assign structural and functional annotations to the ever increasing amount of sequenced proteins, the main approach relies on sequence-based homology search methods, e.g. BLAST or the current state-of-the-art methods based on profile Hidden Markov Models (pHMM), which rely on significant alignments of query sequences to annotated proteins or protein families. While powerful, these approaches do not take coevolution between residues into account. Taking advantage of recent advances in the field of contact prediction, we propose here to represent proteins by Potts models, which model direct couplings between positions in addition to positional composition, and to compare proteins by aligning these models. Due to non-local dependencies, the problem of aligning Potts models is hard and remains the main computational bottleneck for their use.ResultsWe introduce here an Integer Linear Programming formulation of the problem and PPalign, a program based on this formulation, to compute the optimal pairwise alignment of Potts models representing proteins in tractable time. The approach is assessed with respect to a non-redundant set of reference pairwise sequence alignments from SISYPHUS benchmark which have lowest sequence identity (between 3% and 20%) and enable to build reliable Potts models for each sequence to be aligned. This experimentation confirms that Potts models can be aligned in reasonable time (1′37″ in average on these alignments). The contribution of couplings is evaluated in comparison with HHalign and PPalign without couplings. Although Potts models were not fully optimized for alignment purposes and simple gap scores were used, PPalign yields a better mean F1 score and finds significantly better alignments than HHalign and PPalign without couplings in some cases.ConclusionsThese results show that pairwise couplings from protein Potts models can be used to improve the alignment of remotely related protein sequences in tractable time. Our experimentation suggests yet that new research on the inference of Potts models is now needed to make them more comparable and suitable for homology search. We think that PPalign’s guaranteed optimality will be a powerful asset to perform unbiased investigations in this direction.

scholarly journals Selection of sequence motifs and generative Hopfield-Potts models for protein families

2019 ◽  
Author(s):  
Kai Shimagaki ◽  
Martin Weigt
Keyword(s):  
Amino Acid ◽  
Ad Hoc ◽  
Three Dimensional ◽  
Generative Models ◽  
Amino Acid Sequences ◽  
Dimensional Structure ◽  
Sequence Motifs ◽  
Restricted Boltzmann Machines ◽  
Potts Models ◽  
Maximum Entropy Models

Statistical models for families of evolutionary related proteins have recently gained interest: in particular pairwise Potts models, as those inferred by the Direct-Coupling Analysis, have been able to extract information about the three-dimensional structure of folded proteins, and about the effect of amino-acid substitutions in proteins. These models are typically requested to reproduce the one- and two-point statistics of the amino-acid usage in a protein family, i.e. to capture the so-called residue conservation and covariation statistics of proteins of common evolutionary origin. Pairwise Potts models are the maximum-entropy models achieving this. While being successful, these models depend on huge numbers of ad hoc introduced parameters, which have to be estimated from finite amount of data and whose biophysical interpretation remains unclear. Here we propose an approach to parameter reduction, which is based on selecting collective sequence motifs. It naturally leads to the formulation of statistical sequence models in terms of Hopfield-Potts models. These models can be accurately inferred using a mapping to restricted Boltzmann machines and persistent contrastive divergence. We show that, when applied to protein data, even 20-40 patterns are sufficient to obtain statistically close-to-generative models. The Hopfield patterns form interpretable sequence motifs and may be used to clusterize amino-acid sequences into functional sub-families. However, the distributed collective nature of these motifs intrinsically limits the ability of Hopfield-Potts models in predicting contact maps, showing the necessity of developing models going beyond the Hopfield-Potts models discussed here.

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