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Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
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Cited by 543 (11 self)
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The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms are given, one that constructs the Voronoi diagram in O(n log n) time, and another that inserts a new site in O(n) time. Both are based on the use of the Voronoi dual, or Delaunay triangulation, and are simple enough to be of practical value. The simplicity of both algorithms can be attributed to the separation of the geometrical and topological aspects of the problem and to the use of two simple but powerful primitives, a geometric predicate and an operator for manipulating the topology of the diagram. The topology is represented by a new data structure for generalized diagrams, that is, embeddings of graphs in twodimensional manifolds. This structure represents simultaneously an embedding, its dual, and its mirror image. Furthermore, just two operators are sufficient for building and modifying arbitrary diagrams.
How to Eliminate Crossings by Adding Handles or Crosscaps
"... Let c k = cr k (G) denote the minimum number of edge crossings when a graph G is drawn on an orientable surface of genus k. The (orientable) crossing sequence c 0 ; c 1 ; c 2 ; : : : encodes the tradeoff between adding handles and decreasing crossings. We focus on sequences of the type c 0 ? c ..."
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Let c k = cr k (G) denote the minimum number of edge crossings when a graph G is drawn on an orientable surface of genus k. The (orientable) crossing sequence c 0 ; c 1 ; c 2 ; : : : encodes the tradeoff between adding handles and decreasing crossings. We focus on sequences of the type c 0 ? c
Counting Higher Genus Curves with Crosscaps
, 2004
"... We compute all loop topological string amplitudes on orientifolds of local CalabiYau manifolds, by using geometric transitions involving SO/Sp ChernSimons theory, localization on the moduli space of holomorphic maps with involution, and the topological vertex. In particular we count Klein bottles ..."
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Cited by 3 (0 self)
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and projective planes with any number of handles in some CalabiYau orientifolds.
Defense Requirements Portfolio Management
, 2014
"... Improving Trade Visibility and Fidelity in ..."
Orientifolds, Mirror Symmetry and
, 2002
"... We consider orientifolds of CalabiYau 3folds in the context of Type IIA and Type IIB superstrings. We show how mirror symmetry can be used to sum up worldsheet instanton contributions to the superpotential for Type IIA superstrings. The relevant worldsheets have the topology of the disc and ..."
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Cited by 14 (2 self)
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We consider orientifolds of CalabiYau 3folds in the context of Type IIA and Type IIB superstrings. We show how mirror symmetry can be used to sum up worldsheet instanton contributions to the superpotential for Type IIA superstrings. The relevant worldsheets have the topology of the disc and
Duality and Instantons in String Theory
, 1999
"... In these lecture notes duality tests and instanton eects in supersymmetric vacua of string theory are discussed. A broad overview of BPSsaturated terms in the eective actions is rst given. Their role in testing the consistency of duality conjectures as well as discovering the rules of instanton cal ..."
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Cited by 8 (3 self)
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In these lecture notes duality tests and instanton eects in supersymmetric vacua of string theory are discussed. A broad overview of BPSsaturated terms in the eective actions is rst given. Their role in testing the consistency of duality conjectures as well as discovering the rules of instanton calculus in string theory is discussed. The example of heterotic/typeI duality is treated in detail. Thresholds of F terms are used to test the duality as well as to derive rules for calculated with D1brane instantons. We further consider the case of R couplings in N=4 groundstates. Heterotic/type II duality is invoked to predict the heterotic NS5brane instanton corrections to the R threshold. The R couplings of typeII string theory with maximal supersymmetry are analysed and the Dinstanton contributions are described Other applications and open problems are sketched.
The Real Topological String on a local CalabiYau
"... We study the topological string on local P2 with Oplane and Dbrane at its real locus, using three complementary techniques. In the Amodel, we refine localization on the moduli space of maps with respect to the torus action preserved by the antiholomorphic involution. This leads to a computation o ..."
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We study the topological string on local P2 with Oplane and Dbrane at its real locus, using three complementary techniques. In the Amodel, we refine localization on the moduli space of maps with respect to the torus action preserved by the antiholomorphic involution. This leads to a computation of open and unoriented GromovWitten invariants that can be applied to any toric CalabiYau with involution. We then show that the full topological string amplitudes can be reproduced within the topological vertex formalism. We obtain the real topological vertex with trivial fixed leg. Finally, we verify that the same results derive in the Bmodel from the extended holomorphic anomaly equation, together with appropriate boundary conditions. The expansion at the conifold exhibits a gap structure that belongs to a so far unidentified
Results 1  10
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