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Diamond Hierarchies of Arbitrary Dimension
"... Nested simplicial meshes generated by the simplicial bisection decomposition proposed by Maubach [Mau95] have been widely used in 2D and 3D as multiresolution models of terrains and threedimensional scalar fields, They are an alternative to octree representation since they allow generating crackf ..."
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Nested simplicial meshes generated by the simplicial bisection decomposition proposed by Maubach [Mau95] have been widely used in 2D and 3D as multiresolution models of terrains and threedimensional scalar fields, They are an alternative to octree representation since they allow generating crackfree representations of the underlying field. On the other hand, this method generates conforming meshes only when all simplices sharing the bisection edge are subdivided concurrently. Thus, efficient representations have been proposed in 2D and 3D based on a clustering of the simplices sharing a common longest edge in what is called a diamond. These representations exploit the regularity of the vertex distribution and the diamond structure to yield an implicit encoding of the hierarchical and geometric relationships among the triangles and tetrahedra, respectively. Here, we analyze properties of ddimensional diamonds to better understand the hierarchical and geometric relationships among the simplices generated by Maubach’s bisection scheme and derive closedform equations for the number of vertices, simplices, parents and children of each type of diamond. We exploit these properties to yield an implicit pointerless representation for ddimensional diamonds and reduce the number of required neighborfinding accesses from O(d!) to O(d). Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Hierarchy and geometric transformations I.3.6 [Computer Graphics]: Methodology and Techniques—Graphics data structures and data types 1.
Pictures of complete positivity in arbitrary dimension
 In Quantum Programming Languages, Electronic Proceedings in Theoretical Computer Science
, 2011
"... Two fundamental contributions to categorical quantum mechanics are presented. First, we generalize the CPconstruction, that turns any dagger compact category into one with completely positive maps, to arbitrary dimension. Second, we axiomatize when a given category is the result of this constructio ..."
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Cited by 5 (3 self)
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Two fundamental contributions to categorical quantum mechanics are presented. First, we generalize the CPconstruction, that turns any dagger compact category into one with completely positive maps, to arbitrary dimension. Second, we axiomatize when a given category is the result
Spherical Gravitating Systems of Arbitrary Dimension
, 2008
"... We study spherically symmetric solutions to the Einstein field equations under the assumption that the spacetime may possess an arbitrary number of spatial dimensions. The general solution of Synge is extended to describe systems of any dimension. Arbitrary dimension analogues of known four dimensi ..."
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Cited by 1 (0 self)
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We study spherically symmetric solutions to the Einstein field equations under the assumption that the spacetime may possess an arbitrary number of spatial dimensions. The general solution of Synge is extended to describe systems of any dimension. Arbitrary dimension analogues of known four
Bodies of constant width in arbitrary dimension
, 2005
"... We give a number of characterizations of bodies of constant width in arbitrary dimension. As an application, we describe a way to construct a body of constant width in dimension n, one of its (n − 1)dimensional projection being given. We give a number of examples, like a fourdimensional body of con ..."
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Cited by 7 (1 self)
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We give a number of characterizations of bodies of constant width in arbitrary dimension. As an application, we describe a way to construct a body of constant width in dimension n, one of its (n − 1)dimensional projection being given. We give a number of examples, like a fourdimensional body
Equientangled bases in arbitrary dimensions
, 2005
"... For the space of two identical systems of arbitrary dimensions, we introduce a continuous family of bases with the following properties: i) the bases are orthonormal, ii) in each basis, all the states have the same values of entanglement, and iii) they continuously interpolate between the product ba ..."
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Cited by 1 (0 self)
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For the space of two identical systems of arbitrary dimensions, we introduce a continuous family of bases with the following properties: i) the bases are orthonormal, ii) in each basis, all the states have the same values of entanglement, and iii) they continuously interpolate between the product
Freeform Curves on Spheres of Arbitrary Dimension
"... Recursive evaluation procedures based on spherical linear interpolation and stationary subdivision algorithms based on geodesic midpoint averaging are used to construct the analogues on spheres of arbitrary dimension of Lagrange and Hermite interpolation, Bezier and Bspline approximation, CatmullR ..."
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Recursive evaluation procedures based on spherical linear interpolation and stationary subdivision algorithms based on geodesic midpoint averaging are used to construct the analogues on spheres of arbitrary dimension of Lagrange and Hermite interpolation, Bezier and Bspline approximation, Catmull
Dual Linearised Gravity in Arbitrary Dimensions
, 2005
"... Abstract. We construct dual formulation of linearised gravity in first order tetrad formalism in arbitrary dimensions within the path integral framework following the standard duality algorithm making use of the global shift symmetry of the tetrad field. The dual partition function is in terms of th ..."
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Cited by 3 (0 self)
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Abstract. We construct dual formulation of linearised gravity in first order tetrad formalism in arbitrary dimensions within the path integral framework following the standard duality algorithm making use of the global shift symmetry of the tetrad field. The dual partition function is in terms
On blackbrane instability in an arbitrary dimension
, 2004
"... Abstract: The blackhole blackstring system is known to exhibit critical dimensions and therefore it is interesting to vary the spacetime dimension D, treating it as a parameter of the system. We derive the large D asymptotics of the critical, i.e. marginally stable, string following an earlier num ..."
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Cited by 30 (8 self)
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Abstract: The blackhole blackstring system is known to exhibit critical dimensions and therefore it is interesting to vary the spacetime dimension D, treating it as a parameter of the system. We derive the large D asymptotics of the critical, i.e. marginally stable, string following an earlier
Results 11  20
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183,534