Circular Planar Electrical Networks, Split Systems, and Phylogenetic Networks

IF 1.6 2区 数学 Q2 MATHEMATICS, APPLIED
S. Forcey
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引用次数: 0

Abstract

We study a new invariant of circular planar electrical networks, well known to phylogeneticists: the circular split system. We use our invariant to answer some open questions about levels of complexity of networks and their related Kalmanson metrics. The key to our analysis is the realization that certain matrices arising from weighted split systems are studied in another guise: the Kron reductions of Laplacian matrices of planar electrical networks. Specifically we show that a response matrix of a circular planar electrical network corresponds to a unique resistance metric obeying the Kalmanson condition, and thus a unique weighted circular split system. Our results allow interchange of methods: phylogenetic reconstruction using theorems about electrical networks, and circuit reconstruction using phylogenetic techniques.
圆形平面电网络,分裂系统和系统发育网络
我们研究了一个新的圆形平面电网络不变量,这是系统发育学家所熟知的:圆形分裂系统。我们使用我们的不变量来回答一些关于网络及其相关卡曼森度量的复杂程度的开放性问题。我们分析的关键是认识到某些由加权分裂系统产生的矩阵是在另一种伪装下研究的:平面电网络拉普拉斯矩阵的Kron约简。具体来说,我们证明了平面圆形电网的响应矩阵对应于一个符合Kalmanson条件的唯一电阻度量,从而对应于一个唯一加权圆形分裂系统。我们的结果允许交换方法:使用关于电网络的定理进行系统发育重建,以及使用系统发育技术进行电路重建。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
19
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