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The Singularity Set of Optimal Transportation Maps
AbstractOptimal transportation plays an important role in many engineering fields, especially in deep learning. By the Brenier theorem, computing...
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Macroscopic Fundamental Diagram for Train Platforms
The macroscopic fundamental diagram (MFD) relates the flow, density and speed of an entire network. So far, the MFD has been mostly applied to cases...
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A Cap Covering Theorem
A cap of spherical radius α on a unit d -sphere S is the set of points within spherical distance α from a given point on the sphere. Let
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Efficient algorithms for support path with time constraint
Target traversing is an important research topic in wireless sensor networks, with most studies examining coverage issues of the target’s moving...
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How to Cut Corners and Get Bounded Convex Curvature
We describe an algorithm for solving an important geometric problem arising in computer-aided manufacturing. When cutting away a region from a solid...
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Direct Flow Simulation of Objects Represented by Point Clouds
In this chapter, we present a recently proposed approach for performing multiphysics analysis using immersogeometric analysis (IMGA) on complex...
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Analyzing the Squared Distance-to-Measure Gradient Flow System with k-Order Voronoi Diagrams
Point cloud data arises naturally from 3-dimensional scanners, LiDAR sensors, and industrial computed tomography (i.e. CT scans) among other sources....
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Gmsh’s Approach to Robust Mesh Generation of Surfaces with Irregular Parametrizations
This paper proposes a robust and effective approach to overcome a major difficulty associated to surface finite element mesh generation: the handling...
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Wildfire burn scar encapsulation
Wildfires burn annually across the United States (US), which threaten those in close proximity to them. Due to drastic alterations of soil properties...
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Klein Sail and Diophantine Approximation of a Vector
In the papers by V. I. Arnold and his successors based upon the ideas of H. Poincaré and F. Klein, it was the Klein sail associated with an operator...
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Large-Scale Tools
It is clear that the difficulty for spatial systems – including spatial networks – is to go beyond local measures and characterization. This is a...
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Redistricting algorithms
Why not have a computer just draw the best map? For many people, this is the first and only reasonable approach to the problem of gerrymandering. But...
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Transposition of Biomimetical Principles into Generative Design: Example of the Species Campanula patula L
This paper deals with the flower geometry analysis of the species Campanula patula L. (Campanulaceae) and attempts to use a freeform curve to...
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Near optimal minimal convex hulls of disks
The minimal convex hulls of disks problem is to find such arrangements of circular disks in the plane that minimize the length of the convex hull...
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Computing persistent Stiefel–Whitney classes of line bundles
We propose a definition of persistent Stiefel–Whitney classes of vector bundle filtrations. It relies on seeing vector bundles as subsets of some...
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Stable honeycomb structures and temperature based trajectory optimization for wire-arc additive manufacturing
We consider two mathematical problems that are connected and occur in the layer-wise production process of a workpiece using wire-arc additive...
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SU(3) Higher Roots and Their Lattices
After recalling the notion of higher roots (or hyper-roots) associated with “quantum modules” of type (G, k), for G a semi-simple Lie group and k a...
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VerifyRealRoots: A Matlab Package for Computing Verified Real Solutions of Polynomials Systems of Equations and Inequalities
VerifyRealRoots is a Matlab package for computing and verifying real solutions of polynomial systems of equations and inequalities. It calls Bertini...