The Shapley Value of Phylogenetic Trees

Every weighted tree corresponds naturally to a cooperative game that we call a "tree game"; it assigns to each subset of leaves the sum of the weights of the minimal subtree spanned by those leaves. In the context of phylogenetic trees, the leaves are species and this assignment captures the diversity present in the coalition of species considered. We consider the Shapley value of tree games and suggest a biological interpretation. We determine the linear transformation M that shows the dependence of the Shapley value on the edge weights of the tree, and we also compute a null space basis of M. Both depend on the "split counts" of the tree. Finally, we characterize the Shapley value on tree games by four axioms, a counterpart to Shapley's original theorem on the larger class of cooperative games.Comment: References added, and a section (calculating the Shapley value of a tree game from its subtrees) was removed for length reasons (request of referee) and may appear in another paper. 16 pages; related work at http://www.math.hmc.edu/~su/papers.html. Journal of Mathematical Biology, to appear. The original article is available at http://www.springerlink.co

1997 biological surveys of four Southern California artificial reefs: Oceanside #2, Carlsbad, Pacific Beach, and Mission Bay Park

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The Shapley value of phylogenetic trees

Every weighted tree corresponds naturally to a cooperative game that we call a tree game; it assigns to each subset of leaves the sum of the weights of the minimal subtree spanned by those leaves. In the context of phylogenetic trees, the leaves are species and this assignment captures the diversity present in the coalition of species considered. We consider the Shapley value of tree games and suggest a biological interpretation. We determine the linear transformation M that shows the dependence of the Shapley value on the edge weights of the tree, and we also compute a null space basis of M. Finally, we characterize the Shapley value on tree games by five axioms, a counterpart to Shapley's original theorem on the larger class of cooperative games. We also include a brief discussion of the core of tree games.

Constructing Phylogenetic Trees from Subsplits

Phylogenetic trees represent theoretical evolutionary relationships among various species. Mathematically they can be described as weighted binary trees and the leaves represent the taxa being compared. One major problem in mathematical biology is the reconstruction of these trees. We already know that trees on the leaf set X can be uniquely constructed from splits, which are bipartitions of X. The question I explore in this thesis is whether reconstruction of a tree is possible from subsplits, or partial split information. The major result of this work is a constructive algorithm which allows us to determine whether a given set of subsplits will realize a tree and, if so, what the tree looks like

State of Efflux of Scavenging Air through the Scavenging Ports

In order to make clear how the efflux angle changes in a small crankcase scavenged engine cylinder and in a large loop scavenged engine cylinder, the inlet flow pattern in the single cycle model cylinder has been observed by a high speed motion camera. In general, the scavenging air stream is not effluent in the designed direction of the scavenging port at comparatively slight opening, and the efflux angle changes in proportion to port opening advance. In a small crankcase scavenged engine cylinder, to keep the scavenging air stream in the direction of the scavenging port it is effective to incline the scavenging air passage between the crankcase and the cylinder, and to make thicker the cylinder wall where located scavenging port. In a large loop scavenged engine cylinder to coincide the scavenging air stream with the direction of the scavenging port in the early stage of the scavenging, it has an effect to set the guide plate the position of 1/2 at port height

Phytochemical studies on traditional herbal medicines based on the ethnopharmacological information obtained by field studies

Traditional herbal medicines, which have been used in the matured traditional medical systems as well as those have been used in ethnic medical systems, are invaluable resources of drug seeds. Ethnobotanical and ethnopharmacological survey may provide useful information of these herbal medicines, which are valuable for searching new bioactive molecules. From this viewpoint, we have been performing the ethnobotanical and ethnopharmacological field studies in Yunnan Province and Guangxi Zhuang Autonomous Region, China, and Mongolia. Phytochemical studies on traditional herbal medicines were performed based on the information obtained by our ethnobotanical survey. Herbal medicines used in Uzbekistan and Bangladesh were also investigated on the basis of the ethnopharmacological information obtained from collaborative researchers in the respective regions. Some studies were carried out for searching active substance(s) based on bioassay-guided fractionation and isolation. Over 150 new molecules were isolated in these studies, and their various biological activities were also demonstrated. This review summarizes the results of phytochemical studies of those traditional herbal medicines as well as biological activities of the isolated molecules