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Strong Hanani–Tutte on the projective plane
 SIAM JOURNAL ON DISCRETE MATHEMATICS
, 2009
"... If a graph can be drawn in the projective plane so that every two nonadjacent edges cross an even number of times, then the graph can be embedded in the projective plane. ..."
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Cited by 3 (3 self)
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If a graph can be drawn in the projective plane so that every two nonadjacent edges cross an even number of times, then the graph can be embedded in the projective plane.
HananiTutte and Related Results
, 2011
"... We are taking the view that crossings of adjacent edges are trivial, and easily got rid of. ..."
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Cited by 4 (2 self)
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We are taking the view that crossings of adjacent edges are trivial, and easily got rid of.
HananiTutte and Monotone Drawings
"... Abstract. A drawing of a graph is xmonotone if every edge intersects every vertical line at most once and every vertical line contains at most one vertex. Pach and Tóth showed that if a graph has an xmonotone drawing in which every pair of edges crosses an even number of times, then the graph has ..."
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Abstract. A drawing of a graph is xmonotone if every edge intersects every vertical line at most once and every vertical line contains at most one vertex. Pach and Tóth showed that if a graph has an xmonotone drawing in which every pair of edges crosses an even number of times, then the graph has an xmonotone embedding in which the xcoordinates of all vertices are unchanged. We give a new proof of this result and strengthen it by showing that the conclusion remains true even if adjacent edges are allowed to cross oddly. This answers a question posed by Pach and Tóth. Moreover, we show that an extension of this result for graphs with nonadjacent pairs of edges crossing oddly fails even if there exists only one such pair in a graph. 1
HananiTutte, monotone drawings, and levelplanarity
, 2011
"... A drawing of a graph is xmonotone if every edge intersects every vertical line at most once and every vertical line contains at most one vertex. Pach and Tóth showed that if a graph has an xmonotone drawing in which every pair of edges crosses an even number of times, then the graph has an xmonot ..."
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Cited by 2 (1 self)
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A drawing of a graph is xmonotone if every edge intersects every vertical line at most once and every vertical line contains at most one vertex. Pach and Tóth showed that if a graph has an xmonotone drawing in which every pair of edges crosses an even number of times, then the graph has an xmonotone embedding in which the xcoordinates of all vertices are unchanged. We give a new proof of this result and strengthen it by showing that the conclusion remains true even if adjacent edges are allowed to cross each other oddly. This answers a question posed by Pach and Tóth. We show that a further strengthening to a “removing even crossings” lemma is impossible by separating monotone versions of the crossing and the odd crossing number. Our results extend to levelplanarity, which is a wellstudied generalization of xmonotonicity. We obtain a new and simple algorithm to test levelplanarity in quadratic time, and we show that xmonotonicity of edges in the definition of levelplanarity can be relaxed.
Toward a theory of planarity: Hananitutte and planarity variants
 In Graph Drawing, Lecture Notes in Computer Science
, 2013
"... Abstract. We study HananiTutte style theorems for various notions of planarity, including partially embedded planarity, and simultaneous planarity. This approach brings together the combinatorial, computational and algebraic aspects of planarity notions and may serve as a uniform foundation for pla ..."
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Cited by 8 (1 self)
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Abstract. We study HananiTutte style theorems for various notions of planarity, including partially embedded planarity, and simultaneous planarity. This approach brings together the combinatorial, computational and algebraic aspects of planarity notions and may serve as a uniform foundation
Projection Pursuit Regression
 Journal of the American Statistical Association
, 1981
"... A new method for nonparametric multiple regression is presented. The procedure models the regression surface as a sum of general smooth functions of linear combinations of the predictor variables in an iterative manner. It is more general than standard stepwise and stagewise regression procedures, ..."
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Cited by 555 (6 self)
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A new method for nonparametric multiple regression is presented. The procedure models the regression surface as a sum of general smooth functions of linear combinations of the predictor variables in an iterative manner. It is more general than standard stepwise and stagewise regression procedures, does not require the definition of a metric in the predictor space, and lends itself to graphical interpretation.
Surroundscreen projectionbased virtual reality: The design and implementation of the CAVE
, 1993
"... Abstract Several common systems satisfy some but not all of the VR This paper describes the CAVE (CAVE Automatic Virtual Environment) virtual reality/scientific visualization system in detail and demonstrates that projection technology applied to virtualreality goals achieves a system that matches ..."
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Cited by 709 (27 self)
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Abstract Several common systems satisfy some but not all of the VR This paper describes the CAVE (CAVE Automatic Virtual Environment) virtual reality/scientific visualization system in detail and demonstrates that projection technology applied to virtualreality goals achieves a system that matches
Distributed Computing in Practice: The Condor Experience
 Concurrency and Computation: Practice and Experience
, 2005
"... Since 1984, the Condor project has enabled ordinary users to do extraordinary computing. Today, the project continues to explore the social and technical problems of cooperative computing on scales ranging from the desktop to the worldwide computational grid. In this chapter, we provide the history ..."
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Cited by 542 (7 self)
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Since 1984, the Condor project has enabled ordinary users to do extraordinary computing. Today, the project continues to explore the social and technical problems of cooperative computing on scales ranging from the desktop to the worldwide computational grid. In this chapter, we provide
Impulses and Physiological States in Theoretical Models of Nerve Membrane
 Biophysical Journal
, 1961
"... ABSTRACT Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of nonlinear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model " has two variables of state, representing excitabi ..."
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Cited by 496 (0 self)
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excitability and refractoriness, and qualitatively resembles Bonhoeffer's theoretical model for the iron wire model of nerve. This BVP model serves as a simple representative of a class of excitableoscillatory systems including the HodgkinHuxley (HH) model of the squid giant axon. The BVP phase plane
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
Results 1  10
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385,769