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TwoManifold Problems
, 1112
"... Recently, there has been much interest in spectral approaches to learning manifolds— socalled kernel eigenmap methods. These methods have had some successes, but their applicability is limited because they are not robust to noise. To address this limitation, we look at twomanifold problems, in whi ..."
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: each view allows us to suppress noise in the other, reducing bias in the same way that an instrumental variable allows us to remove bias in a linear dimensionality reduction problem. We propose a class of algorithms for twomanifold problems, based on spectral decomposition of cross
Remarks on piecewiselinear algebra
 Paci J. Math
, 1982
"... This note studies some of the basic properties of the category whose objects are finite unions of (open and closed) polyhedra and whose morphisms are (not necessarily continuous) piecewiselinear maps. Introduction * A function f: V —>W between real vector spaces is piecewiselinear (PL) if ther ..."
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Cited by 25 (5 self)
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This note studies some of the basic properties of the category whose objects are finite unions of (open and closed) polyhedra and whose morphisms are (not necessarily continuous) piecewiselinear maps. Introduction * A function f: V —>W between real vector spaces is piecewiselinear (PL
Surface Reconstruction by Voronoi Filtering
 Discrete and Computational Geometry
, 1998
"... We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled ..."
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Cited by 404 (13 self)
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We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled
Algorithms and . . . PIECEWISELINEAR HOMEOMORPHISMS
, 2008
"... The first part (Chapters 2 through 5) studies decision problems in Thompson’s groups F, T, V and some generalizations. The simultaneous conjugacy problem is determined to be solvable for Thompson’s group F and suitable larger groups of piecewiselinear homeomorphisms of the unit interval. We describ ..."
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The first part (Chapters 2 through 5) studies decision problems in Thompson’s groups F, T, V and some generalizations. The simultaneous conjugacy problem is determined to be solvable for Thompson’s group F and suitable larger groups of piecewiselinear homeomorphisms of the unit interval. We
Fast verification of convexity of piecewiselinear surfaces
 CoRR
"... Short Version We show that a realization of a closed connected PLmanifold of dimension n − 1 in R n (n> 3) is the boundary of a convex polyhedron if and only if the interior of each (n − 3)face has a point, which has a neighborhood lying on the boundary of a convex body. This result is derived ..."
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Cited by 1 (0 self)
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Short Version We show that a realization of a closed connected PLmanifold of dimension n − 1 in R n (n> 3) is the boundary of a convex polyhedron if and only if the interior of each (n − 3)face has a point, which has a neighborhood lying on the boundary of a convex body. This result is derived
On Traces of dstresses in the Skeletons of Lower Dimensions of Piecewiselinear dmanifolds
, 2001
"... We show how a dstress on a piecewiselinear realization of an oriented (nonsimplicial, in general) dmanifold in R d naturally induces stresses of lower dimensions on this manifold, and discuss implications of this construction to the analysis of selfstresses in spatial frameworks. The mappings w ..."
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Cited by 2 (0 self)
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We show how a dstress on a piecewiselinear realization of an oriented (nonsimplicial, in general) dmanifold in R d naturally induces stresses of lower dimensions on this manifold, and discuss implications of this construction to the analysis of selfstresses in spatial frameworks. The mappings
Criteria for Balance in Abelian Gain Graphs, with Applications to PiecewiseLinear Geometry
, 2008
"... Consider a gain graph with abelian gain group having no odd torsion. If there is a basis of the graph’s binary cycle space each of whose members can be lifted to a closed walk whose gain is the identity, then the gain graph is balanced, provided that the graph is finite or the group has no nontrivia ..."
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no nontrivial infinitely 2divisible elements. We apply this theorem to deduce a result on the projective geometry of piecewiselinear realizations of celldecompositions of manifolds.
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