Related papers: Complex Tropical Currents, Extremality, and Approx…

The boundary of a 2D topological superconductor can be modeled by a conformal field theory. Here we demonstrate the behaviors of this high level description emerging from a microscopic model at finite temperatures. To achieve that, we…

Temporal logic is a very powerful formalism deeply investigated and used in formal system design and verification. Its application usually reduces to solving specific decision problems such as model checking and satisfiability. In these…

Poleward trends in seasonal-mean latitudes of tropical cyclones (TCs) have been identified in direct observations from 1980 to present. Paleoclimate reconstructions also indicate poleward-equatorward migrations over centennial to millennial…

We consider positive-(1,1) De Rham currents in arbitrary almost complex manifolds and prove the uniqueness of the tangent cone at any point where the density does not have a jump with respect to all of its values in a neighbourhood. Without…

Extratropical cyclones are large-scale weather systems which are often the source of extreme weather events in Northern Europe, often leading to mass infrastructural damage and casualties. Such systems create a local vorticity maxima which…

This article applies the technical framework developed in previous work by the author to discrete admissible covers and their moduli spaces. More precisely, we construct a poic-space that parameterizes the discrete admissible covers after…

We propose a definition of tropical linear series that isolates some of the essential combinatorial properties of tropicalizations of not-necessarily-complete linear series on algebraic curves. The definition combines the Baker-Norine…

Global medium-range weather forecasts suffer occasional failures, often linked to tropical cyclones (TCs). We investigate TC influences on extratropical predictability by comparing forecasts from a physics-based model (ECMWF-IFS) and an…

We give, in Sections 2 and 3, an english translation of: {\it Classes g\'en\'eralis\'ees invariantes}, J. Math. Soc. Japan, 46, 3 (1994), with some improvements and with notations and definitions in accordance with our book: {\it Class…

We give an introduction to Tropical Geometry and prove some results in Tropical Intersection Theory. The first part of this paper is an introduction to tropical geometry aimed at researchers in Algebraic Geometry from the point of view of…

The supercritical region is often described as uniform with no definite transitions. The distinct behaviors of the matter therein (as liquid-like and gas-like), however, suggest ``supercritical boundaries". Here, we provide a mathematical…

Most studies of non-trivial topological systems are carried out in non-interacting models that admit an exact solution. This raises the question, to which extent the consideration of electronic correlations and disorder, present in real…

Global artificial intelligence (AI) models are rapidly advancing and beginning to outperform traditional numerical weather prediction (NWP) models across metrics, yet predicting regional extreme weather such as tropical cyclone (TC)…

We define a natural operation of conditioning of tropical diagrams of probability spaces and show that it is Lipschitz continuous with respect to the asymptotic entropy distance.

Following up on the recently published circuit theory for thermodynamic devices, we consider networks of Thermo-Electric Converters (TECs) in stationary non-equilibrium. Assuming constant thermoelectric properties, the integration over a…

We define arroids as an abstract axiom set encoding the intersection properties of arrangements of curves. The tropicalization of the complement of arrangement of curves meeting pairwise transversely is shown to be determined by the…

We apply methods of tropical optimization to handle problems of rating alternatives on the basis of the log-Chebyshev approximation of pairwise comparison matrices. We derive a direct solution in a closed form, and investigate the obtained…

We define the tropical moduli space of covers of a tropical line in the plane as weighted abstract polyhedral complex, and the tropical branch map recording the images of the simple ramifications. Our main result is the invariance of the…

The notions of convexity and convex polytopes are introduced in the setting of tropical geometry. Combinatorial types of tropical polytopes are shown to be in bijection with regular triangulations of products of two simplices. Applications…

In these notes we survey the tropical intersection theory on R^n by deriving the properties for tropical cycles from the corresponding properties in Chow cohomology. For this we review the stable intersection product introduced by Mikhalkin…