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1,261
Couplings of microstrip square openloop resonators for crosscoupled planar microwave filters
 IEEE Trans. Microwave Theory and Tech
, 1996
"... Abstract — A new type of crosscoupled planar microwave filter using coupled microstrip square openloop resonators is proposed, A method for the rigorous calculation of the coupling coefficients of three basic coupling structure ~ encountered in thk type of filters is developed. Simple empirical mo ..."
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Cited by 49 (3 self)
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Abstract — A new type of crosscoupled planar microwave filter using coupled microstrip square openloop resonators is proposed, A method for the rigorous calculation of the coupling coefficients of three basic coupling structure ~ encountered in thk type of filters is developed. Simple empirical
Transcendentality and crossing
, 2006
"... We discuss possible phase factors for the Smatrix of planar N = 4 gauge theory, leading to modifications at fourloop order as compared to an earlier proposal. While these result in a fourloop breakdown of perturbative BMNscaling, KotikovLipatov transcendentality in the universal scaling function ..."
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Cited by 175 (2 self)
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We discuss possible phase factors for the Smatrix of planar N = 4 gauge theory, leading to modifications at fourloop order as compared to an earlier proposal. While these result in a fourloop breakdown of perturbative BMNscaling, KotikovLipatov transcendentality in the universal scaling
Planar embedding of planar graphs
 Advances in Computing Research
, 1984
"... Planar embedding with minimal area of graphs on an integer grid is an interesting problem in VLSI theory. Valiant [12] gave an algorithm to construct a planar embedding for trees in linear area, he also proved that there are planar graphs that require quadratic area. We fill in a spectrum between Va ..."
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Cited by 31 (1 self)
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Valiant's results by showing that an Nnode planar graph has a planarembedding with area O(NF), where F is a bound on the path length from any node to the exterior face. In particular, an outerplanar graph can be embedded without crossings in linear area. This bound is tight, up to constant factors
Arbitrary topology shape reconstruction from planar cross sections
 Graphical Models and Image Processing
, 1996
"... In computed tomography, magnetic resonance imaging and ultrasound imaging, reconstruction of the 3D object from the 2D scalarvalued slices obtained by the imaging system is di cult because of the large spacings between the 2D slices. The aliasing that results from this undersampling in the directio ..."
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Cited by 85 (12 self)
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In computed tomography, magnetic resonance imaging and ultrasound imaging, reconstruction of the 3D object from the 2D scalarvalued slices obtained by the imaging system is di cult because of the large spacings between the 2D slices. The aliasing that results from this undersampling in the direction orthogonal to the slices leads to two problems known as the correspondence problem and the tiling problem. A third problem, known as the branching problem, arises because of the structure of the objects being imaged in these applications. Existing reconstruction algorithms typically address only one or two of these problems. In this paper, we approach all three of these problems simultaneously. This is accomplished by imposing a set of three constraints on the reconstructed surface and then deriving precise correspondence and tiling rules from these constraints. The constraints ensure that the regions tiled by these rules obey physical constructs and have a natural appearance. Regions which cannot be tiled by these rules without breaking one or more constraints are tiled with their medial axis (edge Voronoi diagram). Our implementation of the above approach generates triangles of 3D isosurfaces from input which is either a set of contour data or a volume of image slices. Results obtained with synthetic and actual medical data are presented. There are still speci c cases in which our new approach can generate distorted results, but these cases are much less likely to occur than those which cause distortions in other tiling approaches. 2 1
On the crossing number of almost planar graphs
 IN PROC. GD ’05, VOLUME 4372 OF LNCS
, 2006
"... Crossing minimization is one of the most challenging algorithmic problems in topological graph theory, with strong ties to graph drawing applications. Despite a long history of intensive research, no practical “good” algorithm for crossing minimization is known (that is hardly surprising, since the ..."
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Cited by 11 (1 self)
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the problem itself is NPcomplete). Even more surprising is how little we know about a seemingly simple particular problem: to minimize the number of crossings in an almost planar graph, that is, a graph with an edge whose removal leaves a planar graph. This problem is in turn a building block in an “edge
Crossing and weighted crossing number of nearplanar graphs
 ALGORITHMICA
, 2009
"... A nonplanar graph G is nearplanar if it contains an edge e such that G − e is planar. The problem of determining the crossing number of a nearplanar graph is exhibited from different combinatorial viewpoints. On the one hand, we develop minmax formulas involving efficiently computable lower and u ..."
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Cited by 11 (2 self)
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A nonplanar graph G is nearplanar if it contains an edge e such that G − e is planar. The problem of determining the crossing number of a nearplanar graph is exhibited from different combinatorial viewpoints. On the one hand, we develop minmax formulas involving efficiently computable lower
On the Computational Complexity of Upward and Rectilinear Planarity Testing (Extended Abstract)
, 1994
"... A directed graph is upward planar if it can be drawn in the plane such that every edge is a monotonically increasing curve in the vertical direction, and no two edges cross. An undirected graph is rectilinear planar if it can be drawn in the plane such that every edge is a horizontal or vertical se ..."
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Cited by 106 (4 self)
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A directed graph is upward planar if it can be drawn in the plane such that every edge is a monotonically increasing curve in the vertical direction, and no two edges cross. An undirected graph is rectilinear planar if it can be drawn in the plane such that every edge is a horizontal or vertical
On the Crossing Number of Almost Planar Graphs
, 2005
"... If G is a plane graph and x, y ∈ V (G), then the dual distance of x and y is equal to the minimum number of crossings of G with a closed curve in the plane joining x and y. Riskin [7] proved that if G0 is a 3connected cubic planar graph, and x, y are its vertices at dual distance d, then the crossin ..."
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Cited by 4 (2 self)
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If G is a plane graph and x, y ∈ V (G), then the dual distance of x and y is equal to the minimum number of crossings of G with a closed curve in the plane joining x and y. Riskin [7] proved that if G0 is a 3connected cubic planar graph, and x, y are its vertices at dual distance d
Results 1  10
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1,261