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Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
, 2003
"... One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a lowdimensional manifold embedded in a highdimensional space. Drawing on the correspondenc ..."
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Cited by 1226 (15 self)
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on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for representing the highdimensional data. The algorithm provides a computationally efficient approach to nonlinear dimensionality
Macroscopic strings as heavy quarks in large N gauge theory and Antide Sitter supergravity
 PHYS. J. C22
"... Maldacena has put forward large N correspondence between superconformal field theories on the brane and antide Sitter supergravity in spacetime. We study some aspects of the correspondence between N = 4 superconformal gauge theory on D3brane and maximal supergravity on adS5 × S5 by introducing mac ..."
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Cited by 508 (1 self)
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Maldacena has put forward large N correspondence between superconformal field theories on the brane and antide Sitter supergravity in spacetime. We study some aspects of the correspondence between N = 4 superconformal gauge theory on D3brane and maximal supergravity on adS5 × S5 by introducing
Laplacian eigenmaps and spectral techniques for embedding and clustering.
 Proceeding of Neural Information Processing Systems,
, 2001
"... Abstract Drawing on the correspondence between the graph Laplacian, the LaplaceBeltrami op erator on a manifold , and the connections to the heat equation , we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in ..."
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Cited by 668 (7 self)
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Abstract Drawing on the correspondence between the graph Laplacian, the LaplaceBeltrami op erator on a manifold , and the connections to the heat equation , we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded
On a Poisson structure on the space of Stokes matrices
 Internat. Math. Res. Notices 1999
"... Abstract: In this paper we study the map associating to a linear differential operator with rational coefficients its monodromy data. The operator is of the form Λ(z) = d V dz − U − z, with one regular and one irregular singularity of Poincaré rank 1, where U is a diagonal and V is a skewsymmetric ..."
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Cited by 19 (0 self)
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n × n matrix. We compute the Poisson structure of the corresponding Monodromy Preserving Deformation Equations (MPDE) on the space of the monodromy data. Preprint SISSA 120/98/FM Monodromy preserving deformation equations (MPDE) of linear differential operators with rational coefficients are known
Renormalization group flows from holography  Supersymmetry and a ctheorem
 ADV THEOR. MATH. PHYS
, 1999
"... We obtain first order equations that determine a supersymmetric kink solution in fivedimensional N = 8 gauged supergravity. The kink interpolates between an exterior antide Sitter region with maximal supersymmetry and an interior antide Sitter region with one quarter of the maximal supersymmetry. ..."
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Cited by 294 (25 self)
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. One eighth of supersymmetry is preserved by the kink as a whole. We interpret it as describing the renormalization group flow in N = 4 superYangMills theory broken to an N = 1 theory by the addition of a mass term for one of the three adjoint chiral superfields. A detailed correspondence is obtained
UC hierarchy and monodromy preserving deformation
, 2010
"... UC hierarchy and monodromy preserving deformation ..."
Physics © by SpringerVerlag 1980 Monodromy and SpectrumPreserving Deformations I
"... Abstract. A method for solving certain nonlinear ordinary and partial differential equations is developed. The central idea is to study monodromy preserving deformations of linear ordinary differential equations with regular and irregular singular points. The connections with isospectral deformation ..."
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Abstract. A method for solving certain nonlinear ordinary and partial differential equations is developed. The central idea is to study monodromy preserving deformations of linear ordinary differential equations with regular and irregular singular points. The connections with isospectral
On linear variational surface deformation methods
"... This survey reviews the recent advances in linear variational mesh deformation techniques. These methods were developed for editing detailed highresolution meshes, like those produced by scanning realworld objects. The challenge of manipulating such complex surfaces is threefold: the deformatio ..."
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Cited by 169 (11 self)
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, such that the global optimization amounts to solving a sparse linear system of equations. We review the different deformation energies and detail preservation techniques that were proposed in the recent years, together with the various techniques to rectify the linearization artifacts. Our goal is to provide
Noncommutative manifolds, the instanton algebra and isospectral deformations
 Comm. Math. Phys
"... We give new examples of noncommutative manifolds that are less standard than the NCtorus or Moyal deformations of R n. They arise naturally from basic considerations of noncommutative differential topology and have nontrivial global features. The new examples include the instanton algebra and the ..."
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Cited by 167 (29 self)
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obtained from this equation as a noncommutative Grassmanian as well as the corresponding notion of admissible morphisms. This space Gr contains the suspension of a NC3sphere intimately related to quantum group deformations SUq(2) of SU(2) but for unusual values (complex values of modulus one
Results 1  10
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1,810