Related papers: Tropical tensor product and beyond
We study the general rational trigonometry of a tetrahedron, based on quadrances, spreads and solid spreads, using vector products associated to an arbitrary symmetric bilinear form over a general field, not of characteristic two. This…
This thesis delves into the geometry of abstract tropical curves, exploring their complete linear system and associated tropical submodules. We establish a lower bound on the dimension of tropical submodules in terms of the Baker-Norine…
In this work, we initiate the study of \emph{Dynamic Tensor Product Regression}. One has matrices $A_1\in \mathbb{R}^{n_1\times d_1},\ldots,A_q\in \mathbb{R}^{n_q\times d_q}$ and a label vector $b\in \mathbb{R}^{n_1\ldots n_q}$, and the…
This is the third part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part III), we introduce and study…
We define and study a lift of the Boardman-Vogt tensor product of operads to bimodules over operads.
We study unital operator spaces endowed with a partially defined product. We give a matrix-norm characterization of such products that allows for a representation theorem where the partial product is realized as composition of operators on…
In this paper I consider the polymorpism of representations of universal algebra and tensor product of representations of universal algebra.
It is well-known that the tensor product of two bialgebras constitutes the binary product in the category of cocommutative bialgebras and morphisms of bialgebras between them. In this paper, we extend this result to triangular bialgebras…
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 show that in a finite tensor category, the tensor product property holds for support varieties if and only if it holds between indecomposable periodic objects. We apply this to certain Hopf algebras in the form of skew group algebras. In…
We derive the implicit equations for certain parametric surfaces in three-dimensional projective space termed tensor product surfaces. Our method computes the implicit equation for such a surface based on the knowledge of the syzygies of…
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 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 extend recent results in order to construct projective resolutions for modules over twisted tensor products of truncated polynomial rings. We begin by taking note of the conditions necessary to think of these algebras as a type of Ore…
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…
Category theory provides a means through which many far-ranging fields of mathematics can be related by their similar structure. In a paper by Robinson [2], this interconnectivity afforded by categorical perspectives allowed for the…
This work concerns the construction and characterization of product kernels for multivariate approximation from a finite set of discrete samples. To this end, we consider composing different component kernels, each acting on a…
We fix the supports A=(A_1,...,A_k) of a list of tropical polynomials and define the tropical resultant TR(A) to be the set of choices of coefficients such that the tropical polynomials have a common solution. We prove that TR(A) is the…
The software TrIm offers implementations of tropical implicitization and tropical elimination, as developed by Tevelev and the authors. Given a polynomial map with generic coefficients, TrIm computes the tropical variety of the image. When…
We first propose the regular sketch-and-project method for solving tensor equations with respect to the popular t-product. Then, three adaptive sampling strategies and three corresponding adaptive sketch-and-project methods are derived. We…