Results 31 to 40 of about 692 (164)
Adjacency for scattering amplitudes from the Gröbner fan
Journal of High Energy Physics, 2023 Scattering amplitudes in planar N $$ \mathcal{N} $$ = 4 super Yang-Mills theory exhibit singularities which reflect various aspects of the cluster algebras associated to the Grassmannians Gr(4, n) and their tropical counterparts.
L. Bossinger, J. M. Drummond, R. Glew
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Mathematics, 2021 We consider a decision-making problem to evaluate absolute ratings of alternatives from the results of their pairwise comparisons according to two criteria, subject to constraints on the ratings.
Nikolai Krivulin
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Algebraic solutions of tropical optimization problems [PDF]
Lobachevskii Journal of Mathematics, 2015 We consider multidimensional optimization problems, which are formulated and solved in terms of tropical mathematics. The problems are to minimize (maximize) a linear or nonlinear function defined on vectors over an idempotent semifield, and may have constraints in the form of linear equations and inequalities. The aim of the paper is twofold: first to
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Enumerative tropical algebraic geometry in ℝ² [PDF]
Journal of the American Mathematical Society, 2005 The paper establishes a formula for enumeration of curves of arbitrary genus in toric surfaces. It turns out that such curves can be counted by means of certain lattice paths in the Newton polygon. The formula was announced earlier in Counting curves via lattice paths in polygons, C. R. Math.
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The Rényi Entropies Operate in Positive Semifields
Entropy, 2019 We set out to demonstrate that the Rényi entropies are better thought of as operating in a type of non-linear semiring called a positive semifield.
Francisco J. Valverde-Albacete +1 more
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Idempotent semigroups and tropical algebraic sets
Journal of the European Mathematical Society, 2012 The tropical semifield, i.e., the real numbers enhanced by the operations of addition and maximum, serves as a base of tropical mathematics. Addition is an abelian group operation, whereas the maximum defines an idempotent semigroup structure. We address the question of the geometry of idempotent semigroups, in particular, tropical algebraic sets ...
Izhakian, Z., Shustin, E.
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Ecography, EarlyView.Despite the growing number of studies on trophic networks in recent decades, there are still important gaps in our understanding of how these networks are structured across broad environmental gradients. These gaps are even greater in some groups of terrestrial vertebrates, such as snakes, requiring a cohesive synthesis of their broader trophic ...
Daniela Pinto‐Coelho +4 more
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Existence and Uniqueness of Homogeneous Linear Equation Solutions in Supertropical Algebra
Contemporary Mathematics and Applications (ConMathA)This research investigates the existence and uniqueness of solutions to homogeneous linear equations in supertropical algebra. We analyze the structure of supertropical matrices to identify the conditions in which nontrivial solutions exist for the ...
Dian Yuliati, Suci Rahmawati
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Triangulations of cyclic polytopes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We give a new description of the combinatorics of triangulations of even-dimensional cyclic polytopes, and of their bistellar flips. We show that the tropical exchange relation governing the number of intersections between diagonals of a polygon and a ...
Steffen Oppermann, Hugh Thomas
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Precision Restoration to Minimize Soil Loss in a Watershed in the Atlantic Forest Domain
Land Degradation &Development, EarlyView.ABSTRACT The Turvo River Watershed, located in the Zona da Mata region of Minas Gerais and part of the Doce River Basin, faces serious problems of erosion and soil degradation, which compromise and reduce the quality of local water resources. Given this scenario, it is essential to implement environmental recovery strategies that prioritize the ...
Rodrigo Nobre Santana +6 more
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