标题: 有根谱系树中的无根夏普利值
Unrooted Shapley Value of Rooted Phylogenetic Trees
作者: 高毓翔
符麦克
Kao, Yu-Hsiang
Michael, Fuchs
应用数学系所
关键字: 谱系树;夏普利值;Phylogenetic trees;Shapley value;Fair proportion index
公开日期: 2017
摘要: 夏普利值 ( Shapley value)在1953年被Llody Shapley提出,在赛局理论 (Cooperative game theory)中是一个相当重要的参数,它在许多科学领域都被应用。近几年来它被建议成一个优先的工具来估算谱系树中的类群的重要性。
在此论文中,我们将会讨论谱系树中三种不同的夏普利值:有根夏普利值,变形的夏普利值和无根夏普利值。前面两个已经被讨论过在Jin and Fuchs (2014) 然后我们会复习一下一些已知结果。特别是他们已经证明变形的有根夏普利值跟fair proportion index有高度的相关性,fair proportion index 在演化生物学中是另一个经常使用的工具。在 Hartmann (2013)中,他们也提出了一些数据证明了他们的理论。
最近发现Hartmann的实验数据中用的是无根夏普利值而不是变形的有根夏普利值。因此我们论文主要的目标是用数值分析还有理论的证明去讨论无根夏普利值和fair proportion index的相关性。
The Shapley value, proposed by Lloyd Shapley in 1953, is an important parameter in cooperative game theory and is widely used in several areas of science. Recently, it was suggested as a prioritization tool for taxa in phylogenetic trees.
In this thesis, we will discuss the three main notions of Shapley values in phylogenetic trees: the rooted Shapley value, the modified rooted Shapley value and the unrooted Shapley value. The first two were discussed in a recent work of Jin and Fuchs (2014) and we will review their results. In particular, they proved that the modified rooted Shapley value is strongly related to the fair proportion index, another commonly used prioritization tool in biodiversity. Moreover, they claimed that this gives a theoretical justification of data presented by Hartmann (2013).
Recently, it was pointed out that Hartmann actually used the unrooted Shapley value instead of the modified rooted Shapley value in his data. Thus, one of the main goal of this thesis is to study numerically and theoretically the relationship between unrooted Shapley value and fair proportion index. Our results give strong support to the common practice in biodiversity of replacing the unrooted Shapley value by the fair proportion index.
URI: http://etd.lib.nctu.edu.tw/cdrfb3/record/nctu/#GT070452226
http://hdl.handle.net/11536/141036
显示于类别:Thesis