Related papers: Tree Topologies along a Tropical Line Segment

Loss tomography has received considerable attention in recent years and a number of estimators have been proposed. Unfortunately, almost all of them are devoted to the tree topology despite the general topology is more common in practice.…

Metric graphs are important models for capturing the structure of complex data across various domains. While much effort has been devoted to extracting geometric and topological features from graph data, computational aspects of metric…

In this paper we investigate an extremal problem on binary phylogenetic trees. Given two such trees $T_1$ and $T_2$, both with leaf-set ${1,2,...,n}$, we are interested in the size of the largest subset $S \subseteq {1,2,...,n}$ of leaves…

Tree representations of (sets of) symmetric binary relations, or equivalently edge-colored undirected graphs, are of central interest, e.g.\ in phylogenomics. In this context symbolic ultrametrics play a crucial role. Symbolic ultrametrics…

We consider the space of complete and separable metric spaces which are equipped with a probability measure. A notion of convergence is given based on the philosophy that a sequence of metric measure spaces converges if and only if all…

Phylogenetic mixtures model the inhomogeneous molecular evolution commonly observed in data. The performance of phylogenetic reconstruction methods where the underlying data is generated by a mixture model has stimulated considerable recent…

This survey consists of two parts. Part 1 is devoted to amoebas. These are images of algebraic subvarieties in the complex torus under the logarithmic moment map. The amoebas have essentially piecewise-linear shape if viewed at large.…

In phylogenetics, tree-based networks are used to model and visualize the evolutionary history of species where reticulate events such as horizontal gene transfer have occurred. Formally, a tree-based network $N$ consists of a phylogenetic…

The algebraic foundation of tropical polynomial algebra provides the framework for the geometric construction of the supplement and the reversal of tropical varieties, thereby inducing a duality of reduced tropical varieties; for classes of…

Tropical algebraic geometry is an active new field of mathematics that establishes and studies some very general principles to translate algebro-geometric problems into purely combinatorial ones. This expository paper gives an introduction…

The Neighbor-Joining algorithm is a popular distance-based phylogenetic method that computes a tree metric from a dissimilarity map arising from biological data. Realizing dissimilarity maps as points in Euclidean space, the algorithm…

We address phylogenetic reconstruction when the data is generated from a mixture distribution. Such topics have gained considerable attention in the biological community with the clear evidence of heterogeneity of mutation rates. In our…

Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply.…

Evolutionary relationships between species are represented by phylogenetic trees, but these relationships are subject to uncertainty due to the random nature of evolution. A geometry for the space of phylogenetic trees is necessary in order…

We study a parametric version of the Fermat-Weber problem with respect to an asymmetric distance function, which occurs naturally in tropical geometry. Our results yield a method for constructing phylogenetic supertrees.

Tropical algebra is an emerging field with a number of applications in various areas of mathematics. In many of these applications appeal to tropical polynomials allows to study properties of mathematical objects such as algebraic varieties…

Phylogenetic networks which are, as opposed to trees, suitable to describe processes like hybridization and horizontal gene transfer, play a substantial role in evolutionary research. However, while non-treelike events need to be taken into…

The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…

Statistically consistent estimation of phylogenetic trees or gene trees is possible if pairwise sequence dissimilarities can be converted to a set of distances that are proportional to the true evolutionary distances. Susko et al. (2004)…

We consider the problem of exploring an unknown tree with a team of $k$ initially colocated mobile agents. Each agent has limited energy and cannot, as a result, traverse more than $B$ edges. The goal is to maximize the number of nodes…