Convexity in tree spaces

B Lin, B Sturmfels, X Tang, R Yoshida - SIAM Journal on Discrete Mathematics, 2017 - SIAM
We study the geometry of metrics and convexity structures on the space of phylogenetic
trees, which is here realized as the tropical linear space of all ultrametrics. The CAT(0) …

Principal component analysis and the locus of the Fréchet mean in the space of phylogenetic trees

TMW Nye, X Tang, G Weyenberg, R Yoshida - Biometrika, 2017 - academic.oup.com
Evolutionary relationships are represented by phylogenetic trees, and a phylogenetic
analysis of gene sequences typically produces a collection of these trees, one for each gene …

Confidence sets for phylogenetic trees

A Willis - Journal of the American Statistical Association, 2019 - Taylor & Francis
Inferring evolutionary histories (phylogenetic trees) has important applications in biology,
criminology, and public health. However, phylogenetic trees are complex mathematical …

[PDF][PDF] Investigations in Hadamard spaces

A Bërdëllima - 2021 - ediss.uni-goettingen.de
This thesis investigates the interplay between geometry and convex analysis in Hadamard
spaces. Formally a Hadamard space is a complete CAT (0) space, ie a metric space of …

Advanced methods for point cloud processing and simplification

P Chmelar, L Rejfek, TN Nguyen, DH Ha - Applied Sciences, 2020 - mdpi.com
Nowadays, mobile robot exploration needs a rangefinder to obtain a large number of
measurement points to achieve a detailed and precise description of a surrounding area …

Improved particle swarm optimization algorithm based on a three-dimensional convex hull for fitting a screw thread central axis

L Lei, Z **e, H Zhu, Y Guan, M Kong, BO Zhang… - IEEE …, 2020 - ieeexplore.ieee.org
To meet the needs of three-dimensional (3D) measurement and to achieve the high-
precision fitting of the central axis of a screw thread, this study performed complex …

Geodesics to characterize the phylogenetic landscape

M Khodaei, M Owen, P Beerli - Plos one, 2023 - journals.plos.org
Phylogenetic trees are fundamental for understanding evolutionary history. However, finding
maximum likelihood trees is challenging due to the complexity of the likelihood landscape …

Recognizing weighted means in geodesic spaces

A Goodwin, AS Lewis, G Lopez-Acedo… - arxiv preprint arxiv …, 2024 - arxiv.org
Geodesic metric spaces support a variety of averaging constructions for given finite sets.
Computing such averages has generated extensive interest in diverse disciplines. Here we …

Maximum likelihood estimation of log-concave densities on tree space

Y Takazawa, T Sei - Statistics and Computing, 2024 - Springer
Phylogenetic trees are key data objects in biology, and the method of phylogenetic
reconstruction has been highly developed. The space of phylogenetic trees is a …

Compact sets and the closure of their convex hulls in CAT (0) spaces

A Bërdëllima - arxiv preprint arxiv:2109.06002, 2021 - arxiv.org
We study the closure of the convex hull of a compact set in a complete CAT (0) space. First
we give characterization results in terms of compact sets and the closure of their convex …