捕获天然和合成DNA双螺旋结构的中心对称矩阵的可嵌入性
Embeddability of centrosymmetric matrices capturing the double-helix structure in natural and synthetic DNA
摘要：
本文讨论了中心对称矩阵的嵌入问题，中心对称矩阵是串对称模型中矩阵的高阶推广。这些模型捕捉到了DNA双螺旋结构所产生的取代对称性。判断转移矩阵是否可嵌入，使我们能够知道所观察到的替代概率是否与齐次连续时间替代模型（如Kimura模型，Jukes-Cantor模型或一般时间可逆模型）一致。另一方面，推广到高阶矩阵的动机是合成生物学的设置，它与不同大小的遗传字母表。
英文摘要：
In this paper, we discuss the embedding problem for centrosymmetric matrices, which are higher order generalizations of the matrices occurring in Strand Symmetric Models. These models capture the substitution symmetries arising from the double helix structure of the DNA. Deciding whether a transition matrix is embeddable or not enables us to know if the observed substitution probabilities are consistent with a homogeneous continuous time substitution model, such as the Kimura models, the Jukes-Cantor model or the general time-reversible model. On the other hand, the generalization to higher order matrices is motivated by the setting of synthetic biology, which works with different sizes of genetic alphabets.
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