Results 1 to 10 of about 939,183 (156)
A Grassmann manifold handbook: basic geometry and computational aspects [PDF]
Advances in Computational Mathematics, 2020 The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems, dynamic low ...
Thomas Bendokat +2 more
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Monotone Simultaneous Paths Embeddings in $\mathbb{R}^d$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 We study the following problem: Given $k$ paths that share the same vertex set, is there a simultaneous geometric embedding of these paths such that each individual drawing is monotone in some direction?
David Bremner +8 more
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Matching solid shapes in arbitrary dimension via random sampling [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We give simple probabilistic algorithms that approximately maximize the volume of overlap of two solid, i.e. full-dimensional, shapes under translations and rigid motions. The shapes are subsets of $ℝ^d$ where $d≥ 2$.
Daria Schymura
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New Bounds for Hypercube Slicing Numbers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 What is the maximum number of edges of the d-dimensional hypercube, denoted by S(d,k), that can be sliced by k hyperplanes? This question on combinatorial properties of Euclidean geometry arising from linear separability considerations in the theory of ...
M. Reza Emamy-Khansary, Martin Ziegler
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The Many Faces of Alternating-Sign Matrices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 I give a survey of different combinatorial forms of alternating-sign matrices, starting with the original form introduced by Mills, Robbins and Rumsey as well as corner-sum matrices, height-function matrices, three-colorings, monotone triangles ...
James Propp
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Tilings of a Domain on a Hexagon Mesh with Balanced 3-Tiles [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 In this article, we study the question of tilings on a hexagon mesh with balanced 3-tiles. This problem has been studied by Conway and Lagarias in [CL90], by studying the tiling groups, in fact a group containing the tiling-groups, and their Cayley ...
Gilles Radenne
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On the Toppling of a Sand Pile [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 In this paper, we provide the first study of the sand pile model SPM(0) where we assume that all the grains are numbered with a distinct integer.We obtain a lower bound on the number of terminal sand piles by establishing a bijection between a subset of ...
Jean-Christophe Novelli +1 more
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An n-Dimensional Generalization of the Rhombus Tiling [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 Several classic tilings, including rhombuses and dominoes, possess height functions which allow us to 1) prove ergodicity and polynomial mixing times for Markov chains based on local moves, 2) use coupling from the past to sample perfectly random tilings,
Joakim Linde +2 more
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Enumerating Triangulations of Convex Polytopes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 A triangulation of a finite point set A in $\mathbb{R}^d$ is a geometric simplicial complex which covers the convex hull of $A$ and whose vertices are points of $A$.
Sergei Bespamyatnikh
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Data-driven reduced-order modelling for blood flow simulations with geometry-informed snapshots [PDF]
Journal of Computational Physics, 2023 Parametric reduced-order modelling often serves as a surrogate method for hemodynamics simulations to improve the computational efficiency in many-query scenarios or to perform real-time simulations.
Dongwei Ye +2 more
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