Related papers: Wave fronts and caustics in the tropical plane
We give a complete description of Green's D relation for the multiplicative semigroup of all n-by-n tropical matrices. Our main tool is a new variant on the duality between the row and column space of a tropical matrix (studied by Cohen,…
This paper deals with the existence, monotonicity, uniqueness and asymptotic behaviour of travelling wavefronts for a class of temporally delayed, spatially nonlocal diffusion equations.
This paper focuses on studying the configuration spaces of graphs realised in $\mathbb C^2$, such that the configuration space is, after normalisation, one dimensional. If this is the case, then the configuration space is, generically, a…
This paper presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are…
We characterize the extendibility of the normal curvature on frontals and we give a representation formula of this type of frontals. Also we give representation formulas for wavefronts on all types of singularities and others sub classes of…
We present a simple and elementary procedure to sketch the tropical conic given by a degree--two homogeneous tropical polynomial. These conics are trees of a very particular kind. Given such a tree, we explain how to compute a defining…
We present a fundamental theory of curves in the affine plane and the affine space, equipped with the general-affine groups ${\rm GA}(2)={\rm GL}(2,{\bf R})\ltimes {\bf R}^2$ and ${\rm GA}(3)={\rm GL}(3,{\bf R})\ltimes {\bf R}^3$,…
We study the moduli space of metric graphs that arise from tropical plane curves. There are far fewer such graphs than tropicalizations of classical plane curves. For fixed genus $g$, our moduli space is a stacky fan whose cones are indexed…
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…
In this paper, we consider weighted counts of tropical plane curves of particular combinatorial type through a certain number of generic points. We give a criterion, derived from tropical intersection theory on the secondary fan, for a…
Pasque et al. showed that using a tropical symmetric metric as an activation function in the last layer can improve the robustness of convolutional neural networks (CNNs) against state-of-the-art attacks, including the Carlini-Wagner…
In this paper we study tropicalization of Grassmannian and linear varieties. In particular, we study the tropical linear spaces cor- responding to the phylogenetic trees. We prove that corresponding to each subtree of the phylogenetic tree…
We show that the counting of rational curves on a complete toric variety that are in general position to the toric prime divisors coincides with the counting of certain tropical curves. The proof is algebraic-geometric and relies on…
We give an overview of recently implemented polymake features for computations in tropical geometry. The main focus is on explicit examples rather than technical explanations. Our computations employ tropical hypersurfaces, moduli of…
Finding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic-numeric computing. Taking a tropical view on this problem leads to efficient preprocessing techniques, applying polyhedral…
Given a rational polyhedral space $X$ (a tropical cycle with boundary, in the sense of Mikhalkin--Rau), one can define tropical vector bundles on $X$ having real or tropical fibers. By restricting attention to bounded rational sections of…
Representing turbulent flow fields in a compact yet physically faithful form remains a central challenge in computational fluid dynamics. We propose a continuous parametric representation based on localized Gaussian primitives, in which the…
Tropical geometry has recently found several applications in the analysis of neural networks with piecewise linear activation functions. This paper presents a new look at the problem of tropical polynomial division and its application to…
We study tropical commuting matrices from two viewpoints: linear algebra and algebraic geometry. In classical linear algebra, there exist various criteria to test whether two square matrices commute. We ask for similar criteria in the realm…
In this paper we construct a tropical moduli space parametrizing roots of divisors on tropical curves. We study the relation between this space and the skeleton of Jarvis moduli space of nets of limit roots on stable curves. We show that…