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FAST VOLUME RENDERING USING A SHEARWARP FACTORIZATION OF THE VIEWING TRANSFORMATION
, 1995
"... Volume rendering is a technique for visualizing 3D arrays of sampled data. It has applications in areas such as medical imaging and scientific visualization, but its use has been limited by its high computational expense. Early implementations of volume rendering used bruteforce techniques that req ..."
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Cited by 542 (2 self)
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Volume rendering is a technique for visualizing 3D arrays of sampled data. It has applications in areas such as medical imaging and scientific visualization, but its use has been limited by its high computational expense. Early implementations of volume rendering used bruteforce techniques that require on the order of 100 seconds to render typical data sets on a workstation. Algorithms with optimizations that exploit coherence in the data have reduced rendering times to the range of ten seconds but are still not fast enough for interactive visualization applications. In this thesis we present a family of volume rendering algorithms that reduces rendering times to one second. First we present a scanlineorder volume rendering algorithm that exploits coherence in both the volume data and the image. We show that scanlineorder algorithms are fundamentally more efficient than commonlyused ray casting algorithms because the latter must perform analytic geometry calculations (e.g. intersecting rays with axisaligned boxes). The new scanlineorder algorithm simply streams through the volume and the image in storage order. We describe variants of the algorithm for both parallel and perspective projections and
The Dantzig selector: statistical estimation when p is much larger than n
, 2005
"... In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = Ax + z, where x ∈ R p is a parameter vector of interest, A is a data matrix with possibly far fewer rows than columns, n ≪ ..."
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Cited by 879 (14 self)
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, where r is the residual vector y − A˜x and t is a positive scalar. We show that if A obeys a uniform uncertainty principle (with unitnormed columns) and if the true parameter vector x is sufficiently sparse (which here roughly guarantees that the model is identifiable), then with very large probability
Ricci Flow with Surgery on ThreeManifolds
"... This is a technical paper, which is a continuation of [I]. Here we verify most of the assertions, made in [I, §13]; the exceptions are (1) the statement that a 3manifold which collapses with local lower bound for sectional curvature is a graph manifold this is deferred to a separate paper, as the ..."
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Cited by 448 (2 self)
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constant scalar curvature one, and I has length 2ǫ −1; here ǫclose refers to C N topology, with N> ǫ −1. A parabolic neighborhood P(x, t, ǫ −1 r, r 2) is called a strong ǫneck, if, after scaling with factor r −2, it is ǫclose to the evolving standard neck, which at each
Limits on superresolution and how to break them
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2002
"... AbstractÐNearly all superresolution algorithms are based on the fundamental constraints that the superresolution image should generate the low resolution input images when appropriately warped and downsampled to model the image formation process. �These reconstruction constraints are normally com ..."
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Cited by 421 (7 self)
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AbstractÐNearly all superresolution algorithms are based on the fundamental constraints that the superresolution image should generate the low resolution input images when appropriately warped and downsampled to model the image formation process. �These reconstruction constraints are normally
Efficient algorithms for pairingbased cryptosystems
, 2002
"... We describe fast new algorithms to implement recent cryptosystems based on the Tate pairing. In particular, our techniques improve pairing evaluation speed by a factor of about 55 compared to previously known methods in characteristic 3, and attain performance comparable to that of RSA in larger ch ..."
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Cited by 367 (24 self)
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We describe fast new algorithms to implement recent cryptosystems based on the Tate pairing. In particular, our techniques improve pairing evaluation speed by a factor of about 55 compared to previously known methods in characteristic 3, and attain performance comparable to that of RSA in larger
The AdS5 × S 5 superstring worldsheet Smatrix and crossing symmetry
, 2008
"... An Smatrix satisying the YangBaxter equation with symmetries relevant to the AdS5 × S 5 superstring has recently been determined up to an unknown scalar factor. Such scalar factors are typically fixed using crossing relations, however due to the lack of conventional relativistic invariance, in thi ..."
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Cited by 228 (6 self)
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An Smatrix satisying the YangBaxter equation with symmetries relevant to the AdS5 × S 5 superstring has recently been determined up to an unknown scalar factor. Such scalar factors are typically fixed using crossing relations, however due to the lack of conventional relativistic invariance
FiveDimensional Warped Geometry with a Bulk Scalar Field
, 2001
"... We explore the diversity of warped metric function in fivedimensional gravity including a scalar field and a 3brane. We point out that the form of the function is determined by a parameter introduced here. For a particular value of the parameter, the warped metric function is smooth without having ..."
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Cited by 5 (1 self)
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We explore the diversity of warped metric function in fivedimensional gravity including a scalar field and a 3brane. We point out that the form of the function is determined by a parameter introduced here. For a particular value of the parameter, the warped metric function is smooth without
Warped geometry of brane worlds
 Class. Quantum Grav
, 2002
"... Abstract We study the dynamical equations for extradimensional dependence of a warp factor and a bulk scalar in 5D brane world scenarios with induced brane metric of constant curvature. These equations are similar to those for the time dependence of the scale factor and a scalar field in 4D cosmol ..."
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Cited by 2 (1 self)
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Abstract We study the dynamical equations for extradimensional dependence of a warp factor and a bulk scalar in 5D brane world scenarios with induced brane metric of constant curvature. These equations are similar to those for the time dependence of the scale factor and a scalar field in 4D
Dynamics of warped compactifications and the shape of the warped landscape
, 2005
"... The dynamics of warped/flux compactifications is studied, including warping effects, providing a firmer footing for investigation of the “landscape.” We present a general formula for the fourdimensional potential of warped compactifications in terms of tendimensional quantities. This allows a syste ..."
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Cited by 77 (2 self)
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, and outline a systematic discussion of their corrections. We show that potentials for mobile branes receive generic contributions inhibiting slowroll inflation. We give a linearized analysis of general scalar perturbations of warped IIB compactifications, revealing new features for both time independent
from Warped Compactification with Branes
, 2000
"... We present a possible explanation for the smallness of the observed cosmological constant using a variant of the RandallSundrum(RS)GoldbergerWise paradigm for a warped extra dimension. In contrast to RS, we imagine that we are living on the positive tension Planck brane, or on a zerotension TeV ..."
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to exponential suppression by the warp factor. The radion is in the millieV mass range, and if we live on a TeV brane its couplings are large enough that it can measurably alter the gravitational force at submillimeter distances. In this case the KaluzaKlein excitations of the graviton can also contribute
Results 1  10
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