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Tropical algebra for noise removal and optimal control
Journal of Low Frequency Noise, Vibration and Active Control, 2023 Algorithms for noise removal are either complex or ineffective, and the optimal control with inequality constrains makes the algorithm even more complex.
Chun-Mei Gong, Jiao Peng, Jing Wang
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Tropical algebra with high-order matrix for multiple-noise removal
Journal of Low Frequency Noise, Vibration and Active Control, 2023 The technology for multiple-noise removal has triggered skyrocketing interest in both mathematics and engineering, and the tropical algebra has laid the foundation for an abundance of noise filters.
Jing Wang
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Symmetric polynomials in tropical algebra semirings [PDF]
Journal of Symbolic Computation, 2019 The growth of tropical geometry has generated significant interest in the tropical semiring in the past decade. However, there are other semirings in tropical algebra that provide more information, such as the symmetrized (max, +), Izhakian-Rowen's extended and supertropical semirings.
Sara Kališnik
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Algebraic Solution of Tropical Best Approximation Problems
Mathematics, 2023 We introduce new discrete best approximation problems, formulated and solved in the framework of tropical algebra, which deals with semirings and semifields with idempotent addition.
Nikolai Krivulin
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Algebraic Solution of Tropical Polynomial Optimization Problems [PDF]
Mathematics, 2021 We consider constrained optimization problems defined in the tropical algebra setting on a linearly ordered, algebraically complete (radicable) idempotent semifield (a semiring with idempotent addition and invertible multiplication).
Nikolai Krivulin
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Analysis of a key exchange protocol based on tropical matrix algebra
Journal of Mathematical Cryptology, 2018 In this paper, we consider a two party key-exchange protocol proposed in [D. Grigoriev and V. Shpilrain, Tropical cryptography, Comm. Algebra 43 (2014), 2624–2632, Section 2], which uses tropical matrix algebra as the platform.
Kotov Matvei, Ushakov Alexander
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Sparse data embedding and prediction by tropical matrix factorization [PDF]
BMC Bioinformatics, 2021 Background Matrix factorization methods are linear models, with limited capability to model complex relations. In our work, we use tropical semiring to introduce non-linearity into matrix factorization models.
Amra Omanović +3 more
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A fractal modification of the tropical algebra for noise removal and optimal control
Journal of Low Frequency Noise, Vibration and Active ControlThis paper proposes a fractal modification of tropical algebra for noise removal and optimal control. Fractal addition, fractal multiplication, and fractal dot product are defined and explained in a fractal space.
Hong-yi Li, Chun-mei Gong
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Tropical linear algebra with the Łukasiewicz T-norm
Fuzzy Sets and Systems, 2015 The max-Lukasiewicz semiring is defined as the unit interval [0,1] equipped with the arithmetics "a+b"=max(a,b) and "ab"=max(0,a+b-1). Linear algebra over this semiring can be developed in the usual way. We observe that any problem of the max-Lukasiewicz linear algebra can be equivalently formulated as a problem of the tropical (max-plus) linear ...
Martin Gavalec +2 more
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Modelling and Closed-Loop Control of Admissions in a Vaccination Center Through Tropical Algebra [PDF]
Journal of Control, Automation and Electrical Systems, 2023 André E De Morais, CARLOS Andrey Maia
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