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The hierarchy problem and new dimensions at a millimeter
, 2008
"... We propose a new framework for solving the hierarchy problem which does not rely on either supersymmetry or technicolor. In this framework, the gravitational and gauge interactions become united at the weak scale, which we take as the only fundamental short distance scale in nature. The observed wea ..."
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Cited by 664 (5 self)
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weakness of gravity on distances> ∼ 1 mm is due to the existence of n ≥ 2 new compact spatial dimensions large compared to the weak scale. The Planck scale MPl ∼ G −1/2 N is not a fundamental scale; its enormity is simply a consequence of the large size of the new dimensions. While gravitons can freely
The large N limit of superconformal field theories and supergravity
, 1998
"... We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of AntideSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and ..."
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Cited by 5631 (20 self)
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field theories. This leads to a new proposal for a definition of Mtheory which could be extended to include five or four noncompact dimensions. 1
The Xtree: An index structure for highdimensional data
 In Proceedings of the Int’l Conference on Very Large Data Bases
, 1996
"... In this paper, we propose a new method for indexing large amounts of point and spatial data in highdimensional space. An analysis shows that index structures such as the R*tree are not adequate for indexing highdimensional data sets. The major problem of Rtreebased index structures is the over ..."
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Cited by 592 (17 self)
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In this paper, we propose a new method for indexing large amounts of point and spatial data in highdimensional space. An analysis shows that index structures such as the R*tree are not adequate for indexing highdimensional data sets. The major problem of Rtreebased index structures
Maxmargin Markov networks
, 2003
"... In typical classification tasks, we seek a function which assigns a label to a single object. Kernelbased approaches, such as support vector machines (SVMs), which maximize the margin of confidence of the classifier, are the method of choice for many such tasks. Their popularity stems both from the ..."
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Cited by 604 (15 self)
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for learning M 3 networks based on a compact quadratic program formulation. We provide a new theoretical bound for generalization in structured domains. Experiments on the task of handwritten character recognition and collective hypertext classification demonstrate very significant gains over previous
Conformal deformation of a Riemannian metric to constant curvature
 J. Diff. Geome
, 1984
"... A wellknown open question in differential geometry is the question of whether a given compact Riemannian manifold is necessarily conformally equivalent to one of constant scalar curvature. This problem is known as the Yamabe problem because it was formulated by Yamabe [8] in 1960, While Yamabe&apos ..."
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Cited by 308 (0 self)
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A wellknown open question in differential geometry is the question of whether a given compact Riemannian manifold is necessarily conformally equivalent to one of constant scalar curvature. This problem is known as the Yamabe problem because it was formulated by Yamabe [8] in 1960, While Yamabe
The Relaxation Schemes for Systems of Conservation Laws in Arbitrary Space Dimensions
 Comm. Pure Appl. Math
, 1995
"... We present a class of numerical schemes (called the relaxation schemes) for systems of conservation laws in several space dimensions. The idea is to use a local relaxation approximation. We construct a linear hyperbolic system with a stiff lower order term that approximates the original system with ..."
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Cited by 250 (21 self)
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with a small dissipative correction. The new system can be solved by underresolved stable numerical discretizations without using either Riemann solvers spatially or a nonlinear system of algebraic equations solver temporally. Numerical results for 1D and 2D problems are presented. The second order
Incremental Online Learning in High Dimensions
 Neural Computation
, 2005
"... Locally weighted projection regression (LWPR) is a new algorithm for incremental nonlinear function approximation in high dimensional spaces with redundant and irrelevant input dimensions. At its core, it employs nonparametric regression with locally linear models. In order to stay computationally e ..."
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Cited by 164 (19 self)
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Locally weighted projection regression (LWPR) is a new algorithm for incremental nonlinear function approximation in high dimensional spaces with redundant and irrelevant input dimensions. At its core, it employs nonparametric regression with locally linear models. In order to stay computationally
A Hybrid Particle Level Set Method for Improved Interface Capturing
 J. Comput. Phys
, 2002
"... In this paper, we propose a new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field. Our method uses Lagrangian marker particles to rebuild the level set in regions which are underresolved. This is ofte ..."
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Cited by 215 (25 self)
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and purely Lagrangian schemes for interface resolution. The method is presented in three spatial dimensions.
Nonlinear Anisotropic Filtering Of MRI Data
, 1992
"... Despite significant improvements in image quality over the past several years, the full exploitation of magnetic resonance image (MRI) data is often limited by low signal to noise ratio (SNR) or contrast to noise ratio (CNR). In implementing new MR techniques, the criteria of acquisition speed and i ..."
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Cited by 198 (16 self)
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. In contrast to acquisitionbased noise reduction methods we propose a postprocess based on anisotropic diffusion. Extensions of this new technique support 3D and multiecho MRI, incorporating higher spatial and spectral dimensions. The procedure overcomes the major drawbacks of conventional filter methods
QCD with one compact spatial dimension
, 2006
"... Abstract: The realization of global symmetries can depend on the geometry of the underlying space. In particular, compactification can lead to spontaneous breaking of such symmetries. Four–dimensional QCD with fundamental representation fermions embedded in a space with one compact spatial dimension ..."
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Abstract: The realization of global symmetries can depend on the geometry of the underlying space. In particular, compactification can lead to spontaneous breaking of such symmetries. Four–dimensional QCD with fundamental representation fermions embedded in a space with one compact spatial
Results 1  10
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2,890