{"title":"Holliday junctions in the set of DNA molecules for new translation-invariant Gibbs measures of the Potts model","authors":"N. M. Khatamov, N. N. Malikov","doi":"10.1134/s0040577924020119","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a DNA molecule as a configuration of the Potts model on paths of the Cayley tree. For this model, we study new translation-invariant Gibbs measures. We find exact values of the parameter establishing the uniqueness of translation-invariant Gibbs measures. Each such measure describes the state (phase) of a set of DNA molecules. These Gibbs measures are used to study probability distributions of the Holliday junctions in the DNA molecules. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1134/s0040577924020119","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a DNA molecule as a configuration of the Potts model on paths of the Cayley tree. For this model, we study new translation-invariant Gibbs measures. We find exact values of the parameter establishing the uniqueness of translation-invariant Gibbs measures. Each such measure describes the state (phase) of a set of DNA molecules. These Gibbs measures are used to study probability distributions of the Holliday junctions in the DNA molecules.
摘要 我们将 DNA 分子视为 Potts 模型在 Cayley 树路径上的配置。针对这一模型，我们研究了新的平移不变吉布斯量。我们找到了参数的精确值，从而确定了平移不变吉布斯量的唯一性。每个这样的度量都描述了一组 DNA 分子的状态（相位）。这些吉布斯度量可用于研究 DNA 分子中霍利迪连接的概率分布。
期刊介绍：
Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems.
Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.
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