论文标题
基于马尔可夫链的采样，用于在最近的邻居热力学模型下探索RNA二级结构
Markov Chain-based Sampling for Exploring RNA Secondary Structure under the Nearest Neighbor Thermodynamic Model
论文作者
论文摘要
我们研究early树作为RNA二级结构的模型，根据最近的邻居热力学模型为每棵树分配能量，并定义树上相应的Gibbs分布。通过Blaine Trees和2-Motzkin路径之间的两次射击，我们设计了Markov链会收敛到Gibbs分布，并通过估计链的光谱间隙来建立快速的混合时间结果。光谱间隙估计值是通过链的一系列分解来确定的，也是通过在戴克路径上其他链的已知混合时间结果建立的。除了结果的数学方面，所得算法还可以用作探索RNA的分支结构及其对能量模型参数的依赖性的工具。附录中提供了实现马尔可夫链的伪代码。
We study plane trees as a model for RNA secondary structure, assigning energy to each tree based on the Nearest Neighbor Thermodynamic Model, and defining a corresponding Gibbs distribution on the trees. Through a bijection between plane trees and 2-Motzkin paths, we design a Markov chain converging to the Gibbs distribution, and establish fast mixing time results by estimating the spectral gap of the chain. The spectral gap estimate is established through a series of decompositions of the chain and also by building on known mixing time results for other chains on Dyck paths. In addition to the mathematical aspects of the result, the resulting algorithm can be used as a tool for exploring the branching structure of RNA and its dependence on energy model parameters. The pseudocode implementing the Markov chain is provided in an appendix.
