[图书][B] Essentials of tropical combinatorics

M Joswig - 2021 - books.google.com
The goal of this book is to explain, at the graduate student level, connections between
tropical geometry and optimization. Building bridges between these two subject areas is …

Information geometry for phylogenetic trees

MK Garba, TMW Nye, J Lueg… - Journal of Mathematical …, 2021 - Springer
We propose a new space of phylogenetic trees which we call wald space. The motivation is
to develop a space suitable for statistical analysis of phylogenies, but with a geometry based …

Tropical principal component analysis on the space of phylogenetic trees

R Page, R Yoshida, L Zhang - Bioinformatics, 2020 - academic.oup.com
Motivation Due to new technology for efficiently generating genome data, machine learning
methods are urgently needed to analyze large sets of gene trees over the space of …

Tropical medians by transportation

A Comăneci, M Joswig - Mathematical Programming, 2024 - Springer
Fermat–Weber points with respect to an asymmetric tropical distance function are studied. It
turns out that they correspond to the optimal solutions of a transportation problem. The …

[HTML][HTML] Massively parallel computation of tropical varieties, their positive part, and tropical Grassmannians

D Bendle, J Böhm, Y Ren, B Schröter - Journal of symbolic computation, 2024 - Elsevier
We present a massively parallel framework for computing tropicalizations of algebraic
varieties which can make use of symmetries using the workflow management system GPI …

Tropical Gaussians: a brief survey

NM Tran - Algebraic statistics, 2020 - msp.org
Tropical mathematics has found many applications in both pure and applied areas, as
documented by a growing number of monographs on its interactions with various other …

Tropical logistic regression model on space of phylogenetic trees

G Aliatimis, R Yoshida, B Boyacı, JA Grant - Bulletin of Mathematical …, 2024 - Springer
Classification of gene trees is an important task both in the analysis of multi-locus
phylogenetic data, and assessment of the convergence of Markov Chain Monte Carlo …

[HTML][HTML] Tropical support vector machines: Evaluations and extension to function spaces

R Yoshida, M Takamori, H Matsumoto, K Miura - Neural Networks, 2023 - Elsevier
Abstract Support Vector Machines (SVMs) are one of the most popular supervised learning
models to classify using a hyperplane in an Euclidean space. Similar to SVMs, tropical …

Tropical geometry of phylogenetic tree space: a statistical perspective

A Monod, B Lin, R Yoshida, Q Kang - arXiv preprint arXiv:1805.12400, 2018 - arxiv.org
Phylogenetic trees are the fundamental mathematical representation of evolutionary
processes in biology. They are also objects of interest in pure mathematics, such as …

Signed tropical halfspaces and convexity

G Loho, M Skomra - arXiv preprint arXiv:2206.13919, 2022 - arxiv.org
We extend the fundamentals for tropical convexity beyond the tropically positive orthant
expanding the theory developed by Loho and V\'egh (ITCS 2020). We study two notions of …