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Fast and perfect sampling of subgraphs and polymer systems [article]

Antonio Blanca and Sarah Cannon and Will Perkins
2022 arXiv   pre-print
We give an efficient perfect sampling algorithm for weighted, connected induced subgraphs (or graphlets) of rooted, bounded degree graphs.  ...  This new perfect sampling algorithm for polymer models gives improved sampling algorithms for spin systems at low temperatures on expander graphs and unbalanced bipartite graphs, among other applications  ...  Acknowledgements This work was carried out as part of the AIM SQuaRE workshop 'Connections between computational and physical phase transitions.'  ... 
arXiv:2202.05907v2 fatcat:ukdw6mr3prgohaghxf67k4x3nu

Fast and Perfect Sampling of Subgraphs and Polymer Systems

Antonio Blanca, Sarah Cannon, Will Perkins, Amit Chakrabarti, Chaitanya Swamy
2022
We give an efficient perfect sampling algorithm for weighted, connected induced subgraphs (or graphlets) of rooted, bounded degree graphs.  ...  This new perfect sampling algorithm for polymer models gives improved sampling algorithms for spin systems at low temperatures on expander graphs and unbalanced bipartite graphs, among other applications  ...  We will address both of these examples here and connect them in a new way. 4:2 Fast and Perfect Sampling of Subgraphs and Polymer Systems We consider a natural sampling problem: given a bounded-degree  ... 
doi:10.4230/lipics.approx/random.2022.4 fatcat:thgctgxpsber5irjnsok5q6w3y

Zeros and approximations of Holant polynomials on the complex plane [article]

Katrin Casel, Philipp Fischbeck, Tobias Friedrich, Andreas Göbel, J.A. Gregor Lagodzinski
2020 arXiv   pre-print
Results of our technique include new approximation and sampling algorithms for a diverse class of Holant polynomials in the low-temperature regime and approximation algorithms for general Holant problems  ...  Our method involves establishing zero-free regions for the partition functions of polymer models and using the most significant terms of the cluster expansion to approximate them.  ...  Acknowledgements The authors would like to thank Heng Guo and Guus Regts for helpful comments on an early draft of this work.  ... 
arXiv:1905.03194v3 fatcat:x6w4p4xyfnce7cm7dvjqfrumc4

Protein Evolution within a Structural Space

Eric J. Deeds, Nikolay V. Dokholyan, Eugene I. Shakhnovich
2003 Biophysical Journal  
We approach this question using lattice polymers as a completely characterized model of this space.  ...  We use this measure of structural relatedness to create a graph of lattice structures and compare this graph (in which nodes are lattice structures and edges are defined using structural similarity) to  ...  At high p O and low Z min this decrease is too fast to allow for construction of a graph with 3500 nodes.  ... 
doi:10.1016/s0006-3495(03)74716-x pmid:14581198 pmcid:PMC1303574 fatcat:vrvh5jjr7jfzbffqklyk323rfe

Graph theoretical analysis of the energy landscape of model polymers

Marco Baiesi, Lorenzo Bongini, Lapo Casetti, Lorenzo Tattini
2009 Physical Review E  
In systems characterized by a rough potential energy landscape, local energetic minima and saddles define a network of metastable states whose topology strongly influences the dynamics.  ...  This method is applied to analyze the topology of the network of metastable states for different polypeptidic sequences in a minimalistic polymer model.  ...  Clementi and A. Mossa for providing us with data. M. B. thanks G Barkema and H. Vocks for useful discussions, and acknowledges financial support from K. U. Leuven grant OT/07/034A.  ... 
doi:10.1103/physreve.80.011905 pmid:19658727 fatcat:7flazsomtzgabfao6t223a7edy

Polymer Dynamics via Cliques: New Conditions for Approximations [article]

Tobias Friedrich and Andreas Göbel and Martin S. Krejca and Marcus Pappik
2020 arXiv   pre-print
polymer models are systems of weighted objects, called polymers, equipped with an incompatibility relation.  ...  Central to the existence of such approximation algorithms are weight conditions of the respective polymer model.  ...  Polymer models have also been used to approximate and sample edge spin systems (holant problems) at low temperatures [4] .  ... 
arXiv:2007.08293v3 fatcat:4x2fqyvakbdlpgxe276q73tzxm

A Near-Linear Time Sampler for the Ising Model [article]

Xiaoyu Chen, Xinyuan Zhang
2022 arXiv   pre-print
We prove the correctness and efficiency of our algorithm by establishing spectral independence of distribution of the random cluster model and the rapid mixing of Glauber dynamics on the random cluster  ...  We give a near-linear time sampler for the Gibbs distribution of the ferromagnetic Ising models with edge activities β > 1 and external fields λ<1 (or symmetrically, λ>1) on general graphs with bounded  ...  ∀S ⊆ V, µ Even though the Glauber dynamics fails to be efficient, there still exist fast algorithms to sample from the Gibbs distribution of the ferromagnetic Ising model.  ... 
arXiv:2207.09391v1 fatcat:q2cvakf4gbfgnmdh7s3xglwrmm

Towards Optimally Multiplexed Applications of Universal Arrays

Amir Ben-Dor, Tzvika Hartman, Richard M. Karp, Benno Schwikowski, Roded Sharan, Zohar Yakhini
2004 Journal of Computational Biology  
The problem of optimizing the universal array to avoid disruptive crosshybridization between universal components of the system was addressed previously.  ...  Our formulation translates this problem into that of covering the vertices of one side of a bipartite graph by a minimum number of balanced subgraphs of maximum degree 1.  ...  Proteins are polymers that are composed of building blocks called amino acids.  ... 
doi:10.1089/1066527041410373 pmid:15285903 fatcat:uh7vgxrgwbaunpsomod3u4fnte

Criteria for extensional necking instability in complex fluids and soft solids. Part II: Imposed tensile stress and force protocols

D. M. Hoyle, S. M. Fielding
2016 Journal of rheology  
We study the necking of a filament of complex fluid or soft solid subject to uniaxial tensile stretching, under conditions of constant imposed stress and force, by means of linear stability analysis and  ...  We discuss the way in which these modes of instability manifest themselves in entangled polymeric fluids, demonstrating four distinct regimes of necking behaviour as a function of stress.  ...  In particular, it arises in models of polymeric flow in which polymer chain stretch is dramatically inhibited: in the Rolie-Poly model of linear entangled polymers with chain stretch disallowed, and in  ... 
doi:10.1122/1.4965037 fatcat:tf3xhfrrwffzlpnbz2cfqxcnqm

Network Structure of Protein Folding Pathways [article]

Erzsebet Ravasz, S. Gnanakaran, Zoltan Toroczkai
2007 arXiv   pre-print
In addition, we predict that the exponent and therefore the structure of the folding network fundamentally changes at high temperatures, as verified by our simulations on the AK peptide.  ...  Here we introduce a network approach to capture the statistical properties of the structure of conformation spaces.  ...  Acknowledgments This work was supported in part by the Department of Energy under contract No. W-7405-ENG-36. Note For supporting information please e-mail: eregan@bidmc.harvard.edu.  ... 
arXiv:0705.0912v1 fatcat:deltwwgyibholghlyre62prkn4

A novel graph-based formulation for characterizing morphology with application to organic solar cells [article]

Olga Wodo and Srikanta Tirthapura and Sumit Chaudhary and Baskar Ganapathysubramanian
2011 arXiv   pre-print
Progress in experimental characterization and computational modeling now allow reconstruction and imaging of the thin film morphology.  ...  In this context, a comprehensive set of computational tools to rapidly quantify and classify the heterogeneous internal structure of thin films will be invaluable in linking process, structure and property  ...  Our graph-based characterization framework is fast and efficient, and a natural method to search the process space.  ... 
arXiv:1106.3536v2 fatcat:qaf2mggkv5gddbbltqkhte4xhm

Independent sets in random subgraphs of the hypercube [article]

Gal Kronenberg, Yinon Spinka
2022 arXiv   pre-print
We study the asymptotic number of independent sets in Q_d,p as d →∞ for a wide range of parameters p, including values of p tending to zero as fast as Clog d/d^1/3, constant values of p, and values of  ...  Let Q_d,p be the random subgraph of the d-dimensional hypercube {0,1}^d, where each edge is retained independently with probability p.  ...  Research of YS was supported in part by NSERC of Canada.  ... 
arXiv:2201.06127v1 fatcat:n6rp2ghk25hnhl3hq7tstu3ctm

Stochastic Generator of Chemical Structure. 3. Reaction Network Generation

Jean-Loup Faulon, Allen G. Sault
2001 Journal of chemical information and computer sciences  
The particukrity of the method is that network generation and mechanism reduction are performed simultaneously using sampling techniques. Our method is tested for hydrocarbon thermal cracking.  ...  This finding offe;5the possibility to investigate complex reacting systems such as those studied in petroleum refining and combustion.  ...  . , and the initial number MP of particule in the system.  ... 
doi:10.1021/ci000029m pmid:11500106 fatcat:leen5hnw2vedlgzbhv2qd6zpzm

Ligation of random oligomers leads to emergence of autocatalytic sequence network [article]

Patrick W Kudella, Alexei V Tkachenko, Sergei Maslov, Dieter Braun
2020 bioRxiv   pre-print
The emergence of longer information-carrying and functional nucleotide polymers from random short strands was a major stepping stone at the dawn of life.  ...  Here, we show how nontrivial sequence patterns emerge in a system of random 12mer DNA sequences subject to enzyme-based templated ligation reaction and temperature cycling.  ...  This allowed for fast turnovers of ligation and enabled the observation of sequence 59 dynamics. 60 RESULTS 61 To test templated elongation of polymers in pools of random sequence oligomers, we prepared  ... 
doi:10.1101/2020.08.18.253963 fatcat:zb7zqaydxnhj5c524qmigzjl7y

Nested sampling for materials

Livia B. Pártay, Gábor Csányi, Noam Bernstein
2021 European Physical Journal B : Condensed Matter Physics  
We describe how NS can be adapted to sample the potential energy surface (PES) of atomistic systems, providing a straightforward approximation for the partition function and allowing the evaluation of  ...  After an overview of the basic method, we describe a number of extensions, including using variable cells for constant pressure sampling, the semi-grand-canonical approach for multicomponent systems, parallelizing  ...  The work of N.B. was supported by the U. S. Office  ... 
doi:10.1140/epjb/s10051-021-00172-1 fatcat:mifoqujpmjb3djbyyvdi5ajxnu
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