Hyperplane arrangements, interval orders, and trees.

A hyperplane arrangement is a finite set of hyperplanes in a real affine space. An especially important arrangement is the braid arrangement, which is the set of all hyperplanes xi - xj = 1, 1 trees. For instance, the number of labeled interval orders that can be obtained from n intervals I1,..., In of generic lengths is counted. There is also discussed an arrangement due to N. Linial whose number of regions is the number of alternating (or intransitive) trees, as defined by Gelfand, Graev, and Postnikov [Gelfand, I. M., Graev, M. I., and Postnikov, A. (1995), preprint]. Finally, a refinement is given, related to counting labeled trees by number of inversions, of a result of Shi [Shi, J.-Y. (1986), Lecture Notes in Mathematics, no. 1179, Springer-Verlag] that a certain deformation of the braid arrangement has (n + 1)n-1 regions.

Calculating the probability of multitaxon evolutionary trees: bootstrappers Gambit.

The reconstruction of multitaxon trees from molecular sequences is confounded by the variety of algorithms and criteria used to evaluate trees, making it difficult to compare the results of different analyses. A global method of multitaxon phylogenetic reconstruction described here, Bootstrappers Gambit, can be used with any four-taxon algorithm, including distance, maximum likelihood, and parsimony methods. It incorporates a Bayesian-Jeffreys'-bootstrap analysis to provide a uniform probability-based criterion for comparing the results from diverse algorithms. To examine the usefulness of the method, the origin of the eukaryotes has been investigated by the analysis of ribosomal small subunit RNA sequences. Three common algorithms (paralinear distances, Jukes-Cantor distances, and Kimura distances) support the eocyte topology, whereas one (maximum parsimony) supports the archaebacterial topology, suggesting that the eocyte prokaryotes are the closest prokaryotic relatives of the eukaryotes.

Trees as Tools in Environmental Improvement; An Analysis of the Contribution of Vegetation to Energy and Water Conservation in the Front Range of Colorado

The Denver metropolitan area is facing rapid population growth that increases the stress on already limited resources. Research and advanced computer modeling show that trees, especially those in urban areas, have significant environmental benefits. These benefits include air quality improvements, energy savings, greenhouse gas reduction, and possible water conservation. This Capstone Project applies statistical methods to analyze a small data set of residential homes and their energy and water consumption, as a function of their individual landscape. Results indicate that tree shade can influence water conservation, and that irrigation methods can be an influential factor as well. The Capstone is a preliminary analysis for future study to be performed by the Institute for Environmental Solutions in 2007.

Common trees / by J. Francis Macbride, Asst. Curator, Taxonomy, Dept. of Botany.

no.11(1936)

Woody plants of the western national parks; containing keys for the identification of trees and shrubs, by Virginia Long Bailey and Harold Edwards Bailey.

no.4