## Search

Now showing items 1-10 of 34

#### Searching for weeds – a GIS tool

(University of Canterbury. Mathematics and Statistics, 2008)

Sampling for rare events, such as a new weed incursion, can be surprisingly efficient
when adaptive, unequal probability survey designs are used. Spatially explicit habitat
models and expert knowledge of weedy species ...

#### The K-Maximum Subarray algorithm as an alternative clustering analysis for the spatial weed aggregation pattern

(University of Canterbury. Computer Science and Software EngineeringUniversity of Canterbury. GeographyUniversity of Canterbury. Mathematics and Statistics, 2008)

Weed invasions can alter the nature of the environment, the surrounding ecosystem and
human activities, and it will cost us to manage and control them. This study introduces
the K-Maximum Subarray Algorithm to investigate ...

#### Distributions of gene tree branch lengths under coalescence

(University of Canterbury. Mathematics and Statistics, 2008)

In Bayesian phylogenetic inference, commonly used prior distributions for branch lengths are the uniform, exponential, and gamma distributions. We derive the exact distributions of branch lengths of gene trees under a fixed ...

#### A New Adaptive Sequential Design for Sampling Rare and Clustered Populations

(University of Canterbury. Mathematics and StatisticsUniversity of Canterbury. Management, 2008)

Designing an efficient large-area survey is a challenge for ecologists. Adaptive sampling designs can be efficient because it ensures survey effort is targeted to subareas of high interest. In two-stage sampling, higher ...

#### Wild triangles in 3-connected matroids

(University of Canterbury. Mathematics and Statistics., 2008)

Let {a, b, c} be a triangle in a 3-connected matroid M. In this paper, we describe the structure of M relative to {a, b, c} when, for
all t in {a, b, c}, either M\t is not 3-connected, or M\t has a 3-separation
that is ...

#### A chain theorem for matroids

(University of Canterbury. Mathematics and Statistics., 2008)

Tutte’s Wheels-and-Whirls Theorem proves that if M is a 3-connected matroid other than a wheel or a whirl, then M has a
3-connected minor N such that |E(M)| - |E(N)| = 1. Geelen and Whittle extended this theorem by showing ...

#### Encoding phylogenetic trees in terms of weighted quartets

(University of Canterbury. Mathematics and Statistics., 2008)

One of the main problems in phylogenetics is to develop systematic
methods for constructing evolutionary or phylogenetic trees. For a set
of species X, an edge-weighted phylogenetic X-tree or phylogenetic tree is
a ...

#### Negative correlation in graphs and matroids

(University of Canterbury. Mathematics and Statistics., 2008)

The following two conjectures arose in the work of Grimmett and Winkler, and Pemantle: the uniformly random forest F and the uniformly random connected subgraph C of a finite graph G have
the edge-negative-association ...

#### Quartet compatibility and the quartet graph

(University of Canterbury. Mathematics and Statistics., 2008)

A collection P of phylogenetic trees is compatible if there exists a single phylogenetic tree that displays each of the trees in P. Despite its computational difficulty, determining the compatibility of P is a fundamental ...

#### Leading order integrability conditions for differential-difference equations

(University of Canterbury. Mathematics and Statistics., 2008)

A necessary condition for the existence of conserved densities, ρ, and fluxes of a
differential-difference equation which depend on q shifts, for q sufficiently large, is
presented. This condition depends on the eigenvalues ...