论文标题
基于对称组的模型的模型特定的马尔可夫嵌入问题
The Model-Specific Markov Embedding Problem for Symmetric Group-Based Models
论文作者
论文摘要
我们研究模型的嵌入性，这是概率理论中著名嵌入问题的变体，除非要求马尔可夫矩阵是速率矩阵的矩阵指数，我们还要求速率矩阵遵循模型结构。我们提供了与基于对称组的系统发育模型相对应的模型可嵌入的马尔可夫矩阵的表征。特别是，我们根据基于对称群体的矩阵的特征值提供必要和充分的条件。为了展示我们在模型嵌入性上的主要结果，我们为Hachimoji模型提供了应用，该模型是合成DNA的八态模型。此外，我们在模型嵌入性上的主要结果使我们能够计算模型可嵌入的马尔可夫矩阵的体积相对于模型中其他相关集合的矩阵的体积。
We study model embeddability, which is a variation of the famous embedding problem in probability theory, when apart from the requirement that the Markov matrix is the matrix exponential of a rate matrix, we additionally ask that the rate matrix follows the model structure. We provide a characterisation of model embeddable Markov matrices corresponding to symmetric group-based phylogenetic models. In particular, we provide necessary and sufficient conditions in terms of the eigenvalues of symmetric group-based matrices. To showcase our main result on model embeddability, we provide an application to hachimoji models, which are eight-state models for synthetic DNA. Moreover, our main result on model embeddability enables us to compute the volume of the set of model embeddable Markov matrices relative to the volume of other relevant sets of Markov matrices within the model.
