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Comparing and computing distances between phylogenetic trees are important biological problems, especially for models where edge lengths play an important role. The geodesic distance measure between two phylogenetic trees with edge lengths is the length of the shortest path between them in the continuous tree space introduced by Billera, Holmes, and… (More)

- Aasa Feragen, Megan Owen, Jens Petersen, Mathilde M. W. Wille, Laura H. Thomsen, Asger Dirksen +1 other
- IPMI
- 2013

Statistical analysis of anatomical trees is hard to perform due to differences in the topological structure of the trees. In this paper we define statistical properties of leaf-labeled anatomical trees with geometric edge attributes by considering the anatomical trees as points in the geometric space of leaf-labeled trees. This tree-space is a geodesic… (More)

- Ezra Miller, Megan Owen, J Scott Provan
- 2012

This paper investigates the computational geometry relevant to calculations of the Fréchet mean and variance for probability distributions on the phylogenetic tree space of Billera, Holmes and Vogtmann, using the theory of probability measures on spaces of nonpositive curvature developed by Sturm. We show that the combinatorics of geodesics with a specified… (More)

- Aasa Feragen, Jens Petersen, Megan Owen, Pechin Lo, Laura H. Thomsen, Mathilde M. W. Wille +2 others
- MICCAI
- 2012

We present a fast and robust supervised algorithm for labeling anatomical airway trees, based on geodesic distances in a geometric tree-space. Possible branch label configurations for a given tree are evaluated based on distances to a training set of labeled trees. In tree-space, the tree topology and geometry change continuously, giving a natural way to… (More)

We present two algorithms for computing the geodesic distance between phylogenetic trees in tree space, as introduced by Billera, Holmes, and Vogtmann (2001). We show that the possible combinatorial types of shortest paths between two trees can be compactly represented by a partially ordered set. We calculate the shortest distance along each candidate path… (More)

We describe an algorithm to compute the geodesics in an arbitrary CAT(0) cubical complex. A key tool is a correspondence between cubical complexes of global non-positive curvature and posets with inconsistent pairs. This correspondence also gives an explicit realization of such a complex as the state complex of a reconfigurable system, and a way to embed… (More)

Let S be a subdivision of the plane into polygonal regions, where each region has an associated positive weight. The weighted region shortest path problem is to determine a shortest path in S between two points s, t ∈ R 2 , where the distances are measured according to the weighted Euclidean metric—the length of a path is defined to be the weighted sum of… (More)

Statistical analysis of magnetic resonance angiography (MRA) brain artery trees is performed using two methods for mapping brain artery trees to points in phylogenetic treespace: cortical landmark correspondence and descendant correspondence. The differences in end-results based on these mappings are highlighted to emphasize the importance of correspondence… (More)

We address an open question of Francis and Steel about phylogenetic networks and trees. They give a polynomial time algorithm to decide if a phylogenetic network, N, is tree-based and pose the problem: given a fixed tree T and network N, is N based on T? We show that it is [Formula: see text]-hard to decide, by reduction from 3-Dimensional Matching (3DM)… (More)