Results 31 to 40 of about 69,312 (204)
Random Translates in Minkowski Sums
, 2023 Suppose that $A$ and $B$ are sets in $\mathbb{R}^d$, and we form the sumset of $A$ with $n$ random points of $B$. Given the volumes of $A$ and $B$, how should we choose them to minimize the expected volume of this sumset? Our aim in this paper is to show that we should take $A$ and $B$ to be Euclidean balls.
Balister, Paul +3 more
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Dynamic Minkowski sums under scaling [PDF]
Computer-Aided Design, 2013 In many common real-world and virtual environments, there are a significant number of repeated objects, primarily varying in size. Similarly, in many complex machines, there are a significant number of parts which also vary in size rather than shape. This repetition saves in both design and production costs.
Evan Behar, Jyh-Ming Lien
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Positive geometry in the diagonal limit of the conformal bootstrap
Journal of High Energy Physics, 2019 We consider the diagonal limit of the conformal bootstrap in arbitrary dimensions and investigate the question if physical theories are given in terms of cyclic polytopes.
Kallol Sen +2 more
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Minkowski metrics in creating universal ranking algorithms [PDF]
Biuletyn Wojskowej Akademii Technicznej, 2014 The paper presents a general procedure for creating the rankings of a set of objects, while the relation of preference based on any ranking function. The analysis was possible to use the ranking functions began by showing the fundamental drawbacks of ...
Andrzej Ameljańczyk
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Generalized associahedra via brick polytopes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We generalize the brick polytope of V. Pilaud and F. Santos to spherical subword complexes for finite Coxeter groups. This construction provides polytopal realizations for a certain class of subword complexes containing all cluster complexes of finite ...
Vincent Pilaud, Christian Stump
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Subleading eikonal, AdS/CFT and double stress tensors
Journal of High Energy Physics, 2019 The eikonal phase which determines the Regge limit of the gravitational scat- tering amplitude of a light particle off a heavy one in Minkowski spacetimes admits an expansion in the ratio of the Schwarzschild radius of the heavy particle to the impact ...
Manuela Kulaxizi +2 more
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Diameter, Decomposability, and Minkowski Sums of Polytopes [PDF]
Canadian Mathematical Bulletin, 2018 AbstractWe investigate how the Minkowski sum of two polytopes affects their graph and, in particular, their diameter. We show that the diameter of the Minkowski sum is bounded below by the diameter of each summand and above by, roughly, the product between the diameter of one summand and the number of vertices of the other.
Deza, Antoine, Pournin, Lionel
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Graviton scattering and a sum rule for the c anomaly in 4D CFT
Journal of High Energy Physics, 2018 4D CFTs have a scale anomaly characterized by the coefficient c, which appears as the coefficient of logarithmic terms in momentum space correlation functions of the energy-momentum tensor.
Marc Gillioz +2 more
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Robust polyhedral Minkowski sums with GPU implementation [PDF]
Computer-Aided Design, 2015 We present a Minkowski sum algorithm for polyhedra based on convolution. We develop robust CPU and GPU implementations, using our ACP strategy to eliminate degeneracy and to enforce a user-specified backward error bound. We test the programs on 45 inputs with an error bound of 1 0 - 8 .
Kyung, Min-HO +2 more
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Cephoids. Minkowski sums of prisms
, 2004 We discuss the structure of those polytopes in /R/n+ that are Minkowski sums of prisms. A prism is the convex hull of the origin and "n" positive multiples of the unit vectors. We characterize the defining outer surface of such polytopes by describing the shape of all maximal faces.
Pallaschke, Diethard +1 more
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