Foundations of the Wald Space for Phylogenetic Trees

Evolutionary relationships between species are represented by phylogenetic trees, but these relationships are subject to uncertainty due to the random nature of evolution. A geometry for the space of phylogenetic trees is necessary in order to properly quantify this uncertainty during the statistical analysis of collections of possible evolutionary trees inferred from biological data. Recently, the wald space has been introduced: a length space for trees which is a certain subset of the manifold of symmetric positive definite matrices. In this work, the wald space is introduced formally and its topology and structure is studied in detail. In particular, we show that wald space has the topology of a disjoint union of open cubes, it is contractible, and by careful characterization of cube boundaries, we demonstrate that wald space is a Whitney stratified space of type (A). Imposing the metric induced by the affine invariant metric on symmetric positive definite matrices, we prove that wald space is a geodesic Riemann stratified space. A new numerical method is proposed and investigated for construction of geodesics, computation of Fr\'echet means and calculation of curvature in wald space. This work is intended to serve as a mathematical foundation for further geometric and statistical research on this space.Comment: 42 pages, 15 figure

Economics education and value change: The role of program-normative homogeneity and peer influence

In the light of corporate scandals and the recent financial crisis, there has been an increased interest in the impact of business education on the value orientations of graduates. Yet our understanding of how students' values change during their time at business school is limited. In this study,weinvestigate the effects of variations in the normative orientations of economics programs. We argue that interaction among economics students constitutes a key mechanism of value socialization, the effects of which are likely to vary across more-or-less normatively homogeneous economics programs. In normatively homogeneous programs, students are particularly likely to adopt economics values as a result of peer interaction. We specifically explore changes in power, hedonism, and self-direction values in a 2-year longitudinal study of economics students (N 5 197) in a normatively homogeneous and two normatively heterogeneous economics programs. As expected, for students in a normatively homogeneous economics program, interaction with peers was linked with an increase in power and hedonism values, and a decrease in self-direction values. Our findings highlight the interplay between program normative homogeneity and peer interaction as an important factor in value socialization during economics education and have important practical implications for business school leaders