Numerical Explorations of Feasibility Algorithms for Finding Points in the Intersection of Finite Sets

Abstract We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory. We argue that connections between cluster algebras and tropical geometry provide a natural language for postulating a finite alphabet for scattering amplitudes beyond six and seven points where the corresponding Grassmannian cluster algebras are finite. As well as generating natural finite sets of letters, the tropical fans we discuss provide letters containing square roots. Remarkably, the minimal fan we consider provides all the square root letters recently discovered in an explicit two-loop eight-point NMHV calculation.

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Blind Separation for Multiple Moving Sources with Labeled Random Finite Sets

IEEE/ACM Transactions on Audio Speech and Language Processing ◽

10.1109/taslp.2021.3087003 ◽

2021 ◽

pp. 1-1

Author(s):

Jonah Ong ◽

Ba Tuong Vo ◽

Sven Erik Nordholm

Keyword(s):

Blind Separation ◽

Finite Sets ◽

Moving Sources ◽

Random Finite Sets

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Representation and manipulation of finite sets

ACM SIGAPL APL Quote Quad ◽

10.1145/586169.586171 ◽

1980 ◽

Vol 10 (4) ◽

pp. 8-12 ◽

Cited By ~ 1

Author(s):

B. L. McAllister

Keyword(s):

Finite Sets

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New refinements of the discrete Jensen’s inequality generated by finite or infinite permutations

Aequationes Mathematicae ◽

10.1007/s00010-019-00696-z ◽

2019 ◽

Vol 94 (6) ◽

pp. 1109-1121

Author(s):

László Horváth

Keyword(s):

Banach Spaces ◽

Jensen’S Inequality ◽

Vector Spaces ◽

Real Vector ◽

Finite Sets ◽

Jensen's Inequality

AbstractIn this paper some new refinements of the discrete Jensen’s inequality are obtained in real vector spaces. The idea comes from some former refinements determined by cyclic permutations. We essentially generalize and extend these results by using permutations of finite sets and bijections of the set of positive numbers. We get refinements of the discrete Jensen’s inequality for infinite convex combinations in Banach spaces. Similar results are rare. Finally, some applications are given on different topics.

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