Related papers: Solving one-sided linear systems over symmetrized …
We introduce a scheme-theoretic enrichment of the principal objects of tropical geometry. Using a category of semiring schemes, we construct tropical hypersurfaces as schemes over idempotent semirings such as $\mathbb{T} = (\mathbb{R}\cup…
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…
Tropical linear algebra has been recently put forward by Grigoriev and Shpilrain as a promising platform for implementation of protocols of Diffie-Hellman and Stickel type. Based on the CSR expansion of tropical matrix powers, we suggest a…
We consider discrete best approximation problems in the setting of tropical algebra, which is concerned with the theory and application of algebraic systems with idempotent operations. Given a set of input--output pairs of an unknown…
Speyer recognized that matroids encode the same data as a special class of tropical linear spaces and Shaw interpreted tropically certain basic matroid constructions; additionally, Frenk developed the perspective of tropical linear spaces…
A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the…
A new multidimensional optimization problem is considered in the tropical mathematics setting. The problem is to minimize a nonlinear function defined on a finite-dimensional semimodule over an idempotent semifield and given by a conjugate…
Semiconstrained systems were recently suggested as a generalization of constrained systems, commonly used in communication and data-storage applications that require certain offending subsequences be avoided. In an attempt to apply…
We describe a new approach based on tropical optimization techniques to solve the problem of rating alternatives from pairwise comparison data. The problem is formulated to approximate, in the log-Chebyshev sense, pairwise comparison…
We study the last fall degrees of {\em semi-local} polynomial systems, and the computational complexity of solving such systems for closed-point and rational-point solutions, where the systems are defined over a finite field. A semi-local…
We address a cryptanalysis of two protocols based on the supposed difficulty of discrete logarithm problem on (semi) groups of matrices over a group ring. We can find the secret key and break entirely the protocols.
Tropical and idempotent analysis with their relations to the Hamilton-Jacobi and matrix Bellman equations are discussed. Some dequantization procedures are important in tropical and idempotent mathematics. In particular, the…
We consider two basic algorithmic problems concerning tuples of (skew-)symmetric matrices. The first problem asks to decide, given two tuples of (skew-)symmetric matrices $(B_1, \dots, B_m)$ and $(C_1, \dots, C_m)$, whether there exists an…
We propose a public key encryption cryptosystem based on solutions of linear equation systems with predefinition of input parameters through shared secret computation for factorizable substitutions. The existence of multiple equivalent…
In the present paper we study the existence of solutions for some classes of singular systems involving the p(x) and q(x) Laplacian operators. The approach is based on bifurcation theory and subsupersolution method for systems of…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
A symmetric encryption method based on properties of quasicrystals is proposed. The advantages of the cipher are strict aperiodicity and everywhere discontinuous property as well as the speed of computation, simplicity of implementation and…
In this paper, we study linear programming based approaches to the maximum matching problem in the semi-streaming model. The semi-streaming model has gained attention as a model for processing massive graphs as the importance of such graphs…
We study the expressivity and computational aspects of first-order logic and its extensions in the semiring semantics developed by Gr\"adel and Tannen. We characterize the complexity of model checking and data complexity of first-order…
We study the symmetric tensor rank of multiplication over finite field extensions using linearized polynomials. Via field trace, symmetric linearized polynomials are identified with symmetric bilinear forms and symmetric matrices, allowing…