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Tropical geometry and algebraic cycles

Tropical geometry and algebraic cycles
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Tropical Arithmetic and Matrix Algebra

Communications in Algebra, 2009
This article introduces a new structure of commutative semiring, generalizing the tropical semiring, and having an arithmetic that modifies the standard tropical operations, i.e., summation and maximum. Although our framework is combinatorial, notions of regularity and invertibility arise naturally for matrices over this semiring; we show that a ...
Zur Izhakian
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On the numerical range in tropical algebra

Linear and Multilinear Algebra, 2018
ABSTRACTWe introduce the concept of numerical range in tropical linear algebra, explore its properties and show in particular that it contains all the tropical eigenvalues.
Hanieh Tavakolipour, Fatemeh Shakeri
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Computer Algebra Methods in Tropical Geometry

2010
Tropical geometry is a young field of mathematics which allows to study properties of objects from algebraic geometry with the aid of methods from discrete mathematics, like convex geometry and combinatorics. There are different ways to introduce tropical varieties and to derive the connection between these and their algebraic counterparts.We use a way,
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Algebraic, tropical, and fuzzy geometry

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2011
Fuzzy rings (not directly related to intuitionistic fuzzy rings) were introduced by the first author in [Adv. Math. 59, 97--123 (1986; Zbl 0656.05025)] as a tool to study matroids. In the present paper, the authors establish basic notions of algebraic geometry over arbitrary fuzzy rings, in order to unify the two following special cases.
Dress, Andreas, Wenzel, Walter
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Tropical Algebra and Algebraic Topology of Deep Neural Networks

2020
We present a theoretical and empirical study of feedforward neural networks using tropical algebra and topological data analysis. We show how examining neural networks through the lens of these two disciplines yields insights into their operation and efficacy.
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Tropical algebra

2021
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A closer look at the tropical cryptography

International Journal of Computer Mathematics: Computer Systems Theory, 2021
Delaram Kahrobaei
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Tropical algebra based adaptive filter for noise removal in digital image

Multimedia Tools and Applications, 2020
Achmad Abdurrazzaq, Ismail Mohd, Ahmad Kadri Junoh   +2 more
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On the tropical discrete logarithm problem and security of a protocol based on tropical semidirect product

Communications in Algebra, 2022
Sergei Sergeev
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