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首页> 外文期刊>SIAM Journal on Discrete Mathematics >DISTINGUISHED MINIMAL TOPOLOGICAL LASSOS
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DISTINGUISHED MINIMAL TOPOLOGICAL LASSOS

机译：最小拓扑拓扑

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The ease with which genomic data can now be generated using Next Generation Sequencing technologies combined with a wealth of legacy data holds great promise for exciting new insights into the evolutionary relationships between and within the kingdoms of life. At the subspecies level (e.g., varieties or strains) dendograms, that is, certain edge-weighted rooted trees whose leaves are the elements of a set X of organisms under consideration, are often used to represent those relationships. As is well known, dendrograms can be uniquely reconstructed from distances provided all distances on X are known. More often than not, real biological datasets do not satisfy this assumption, implying that the sought dendrogram need not be uniquely determined by the available distances with regard to topology, edge-weighting, or both. To better understand the structural properties a set L subset of ((X)(2)) has to satisfy to overcome this problem, various types of lassos have been introduced. Here, we focus on the question of when a lasso uniquely determines the topology of a dendrogram; that is, it is a topological lasso for its underlying tree. We show that any set-inclusion minimal topological lasso for such a tree T can be transformed into a structurally nice minimal topological lasso for T. Calling such a lasso a distinguished minimal topological lasso for T, we characterize it in terms of the novel concept of a cluster marker map for T. In addition, we present novel results concerning the heritability of such lassos in the context of the subtree and supertree problems.
机译：现在，利用新一代测序技术结合大量遗留数据可以轻松生成基因组数据，这为激发人们对生命王国之间及其内部进化关系的新见解带来了广阔前景。在亚种水平（例如，变种或品系）的树状图，即某些边缘加权的有根树木，其叶子是所考虑的一组生物的元素，通常被用来表示这些关系。众所周知，只要已知X上的所有距离，就可以根据距离唯一地重建树状图。实际的生物学数据集通常不满足此假设，这意味着所需的树状图无需通过拓扑，边缘权重或两者的可用距离来唯一确定。为了更好地理解（（X）（2））的集合L子集以克服此问题，已引入了各种类型的套索。在这里，我们重点关注套索何时唯一确定树状图拓扑的问题。也就是说，它是其基础树的拓扑套索。我们显示了这样一棵树T的任何集合包含最小拓扑套索都可以转化为T的结构良好的最小拓扑套索。我们称这种套索为T的杰出最小拓扑套索，我们根据T的新概念对其进行了表征。此外，我们在子树和父树问题的背景下提出了有关这种套索的遗传力的新结果。

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