Related papers: Tropical medians by transportation
There is a long tradition of the axiomatic study of consensus methods in phylogenetics that satisfy certain desirable properties. One recently-introduced property is associative stability, which is desirable because it confers a…
The paper focuses on a multidimensional optimization problem, which is formulated in terms of tropical mathematics and consists in minimizing a nonlinear objective function subject to linear inequality constraints. To solve the problem, we…
We define transversal tropical triangles (affine and projective) and characterize them via six inequalities to be satisfied by the coordinates of the vertices. We prove that the vertices of a transversal tropical triangle are tropically…
Using the interpretation of the ultradiscretization procedure as a non-Archimedean valuation, we use results of tropical geometry to show how roots and poles manifest themselves in piece-wise linear systems as points of…
As a new concept tropical halfspaces are introduced to the (linear algebraic) geometry of the tropical semiring (R,min,+). This yields exterior descriptions of the tropical polytopes that were recently studied by Develin and Sturmfels in a…
We model the formation of multi-layer transportation networks as a multi-objective optimization process, where service providers compete for passengers, and the creation of routes is determined by a multi-objective cost function encoding a…
In the last few years there has been a growing interest towards methods for statistical inference and learning based on computational geometry and, notably, tropical geometry, that is, the study of algebraic varieties over the min-plus…
We propose to study the tropical geometry specifically arising from convergent Hahn series in multiple indeterminates. One application is a new view on stable intersections of tropical hypersurfaces. Another one is perturbations of rank one…
Optimal transport has been used extensively in resource matching to promote the efficiency of resources usages by matching sources to targets. However, it requires a significant amount of computations and storage spaces for large-scale…
The tree metric theorem provides a combinatorial four point condition that characterizes dissimilarity maps derived from pairwise compatible split systems. A similar (but weaker) four point condition characterizes dissimilarity maps derived…
An unconstrained optimization problem is formulated in terms of tropical mathematics to minimize a functional that is defined on a vector set by a matrix and calculated through multiplicative conjugate transposition. For some particular…
The presence of reticulate evolutionary events in phylogenies turn phylogenetic trees into phylogenetic networks. These events imply in particular that there may exist multiple evolutionary paths from a non-extant species to an extant one,…
Distance-based phylogenetic algorithms attempt to solve the NP-hard least squares phylogeny problem by mapping an arbitrary dissimilarity map representing biological data to a tree metric. The set of all dissimilarity maps is a Euclidean…
In recent years a series of remarkable advances in tropical geometry and in non-archimedean geometry have brought new insights to the moduli theory of algebraic curves and their Jacobians. The goal of this survey, an expanded version of my…
We consider a PDE approach to numerically solving the optimal transportation problem on the sphere. We focus on both the traditional squared geodesic cost and a logarithmic cost, which arises in the reflector antenna design problem. At each…
Tropical roots of tropical polynomials have been previously studied and used to localize roots of classical polynomials and eigenvalues of matrix polynomials. We extend the theory of tropical roots from tropical polynomials to tropical…
Asymptotic properties of matrices are, in general, difficult to analyze with classical mathematical techniques. In very specific cases, there is a well-known connection between the asymptotic behavior of a matrix's leading eigenvector and…
We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…
Much evidence from biological theory and empirical data indicates that, gene tree, phylogenetic trees reconstructed from different genes (loci), do not have to have exactly the same tree topologies. Such incongruence between gene trees…
Tropical Nevanlinna theory studies value distribution of continuous piecewise linear functions of a real variable. In this paper, we use the reasoning from tropical Nevanlinna theory to present tropical counterparts of some classical…