scholarly journals Potts Models with a Defect Line

2018 ◽  
Vol 362 (1) ◽  
pp. 55-106 ◽  
Author(s):  
Sébastien Ott ◽  
Yvan Velenik
Keyword(s):  
1980 ◽  
Vol 170 (3) ◽  
pp. 409-432 ◽  
Author(s):  
Paul Ginsparg ◽  
Yadin Y. Goldschmidt ◽  
Jean-Bernard Zuber
Keyword(s):  

2014 ◽  
Vol 31 (7) ◽  
pp. 070503 ◽  
Author(s):  
Shun Wang ◽  
Zhi-Yuan Xie ◽  
Jing Chen ◽  
Bruce Normand ◽  
Tao Xiang

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

2006 ◽  
Vol 06 (04) ◽  
pp. L379-L386
Author(s):  
STEVEN WU

We study defect-line dynamics in a 2-D spiral-wave pair in the Rössler model for its underlying local dynamics in period-N and chaotic regimes with a single bifurcation parameter κ. We find that a spiral wave pair is always stable across the period-doubling cascade and in the chaotic regime. When N ≥ 2 defect lines appear spontaneously and a loop exchange occurs across the defect line. There exists a "critical point" κ c below and above which the time-averaged total length of defect lines L converges to almost constant but different values L1 and L2. When κ > κ c defect lines show large fluctuations due to creation and annihilation processes.


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

2020 ◽  
Author(s):  
Hugo Talibart ◽  
François Coste

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.


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