Results 1  10
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1,789
Fivebranes, Membranes And NonPerturbative String Theory
, 1995
"... Nonperturbative instanton corrections to the moduli space geometry of type IIA string theory compactified on a CalabiYau space are derived and found to contain order e \Gamma1=g s contributions, where g s is the string coupling. The computation reduces to a weighted sum of supersymmetric extrema ..."
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Cited by 387 (6 self)
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Nonperturbative instanton corrections to the moduli space geometry of type IIA string theory compactified on a CalabiYau space are derived and found to contain order e \Gamma1=g s contributions, where g s is the string coupling. The computation reduces to a weighted sum of supersymmetric
Stable Distributions, Pseudorandom Generators, Embeddings and Data Stream Computation
, 2000
"... In this paper we show several results obtained by combining the use of stable distributions with pseudorandom generators for bounded space. In particular: ffl we show how to maintain (using only O(log n=ffl 2 ) words of storage) a sketch C(p) of a point p 2 l n 1 under dynamic updates of its coo ..."
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Cited by 324 (13 self)
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coordinates, such that given sketches C(p) and C(q) one can estimate jp \Gamma qj 1 up to a factor of (1 + ffl) with large probability. This solves the main open problem of [10]. ffl we obtain another sketch function C 0 which maps l n 1 into a normed space l m 1 (as opposed to C), such that m = m
Laplacian
, 2003
"... We present sharp lower bounds for eigenvalues of the onedimensional pLaplace operator. The method of proof is rather elementary, based on a suitable generalization of the Lyapunov inequality. 1. ..."
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We present sharp lower bounds for eigenvalues of the onedimensional pLaplace operator. The method of proof is rather elementary, based on a suitable generalization of the Lyapunov inequality. 1.
Orbihedra Of Nonpositive Curvature
 Progress in Mathematics
, 1995
"... . A 2dimensional orbihedron of nonpositive curvature is a pair (X; \Gamma), where X is a 2dimensional simplicial complex with a piecewise smooth metric such that X has nonpositive curvature in the sense of Alexandrov and Busemann and \Gamma is a group of isometries of X which acts properly disc ..."
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Cited by 252 (10 self)
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. A 2dimensional orbihedron of nonpositive curvature is a pair (X; \Gamma), where X is a 2dimensional simplicial complex with a piecewise smooth metric such that X has nonpositive curvature in the sense of Alexandrov and Busemann and \Gamma is a group of isometries of X which acts properly
Global Versus Local Methods in Nonlinear Dimensionality Reduction
, 2003
"... Recently proposed algorithms for nonlinear dimensionality reduction fall broadly into two categories which have different advantages and disadvantages: global (Isomap [1]), and local (Locally Linear Embedding [2], Laplacian Eigenmaps [3]). We present two variants of Isomap which combine the adva ..."
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Cited by 208 (6 self)
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Recently proposed algorithms for nonlinear dimensionality reduction fall broadly into two categories which have different advantages and disadvantages: global (Isomap [1]), and local (Locally Linear Embedding [2], Laplacian Eigenmaps [3]). We present two variants of Isomap which combine
Inequalities for eigenfunctions of the pLaplacian
"... 1 / 57 Barkat Bhayo Inequalities for eigenfunctions of the pLaplacian Motivated by the work of P. Lindqvist, we study eigenfunctions sinp of the onedimensional pLaplace operator, and prove several inequalities for these and panalogues of other trigonometric functions and their inverse functions. ..."
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Cited by 6 (4 self)
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1 / 57 Barkat Bhayo Inequalities for eigenfunctions of the pLaplacian Motivated by the work of P. Lindqvist, we study eigenfunctions sinp of the onedimensional pLaplace operator, and prove several inequalities for these and panalogues of other trigonometric functions and their inverse functions
Spectral partitioning works: planar graphs and finite element meshes, in:
 Proceedings of the 37th Annual Symposium on Foundations of Computer Science,
, 1996
"... Abstract Spectral partitioning methods use the Fiedler vectorthe eigenvector of the secondsmallest eigenvalue of the Laplacian matrixto find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to wo ..."
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Cited by 201 (10 self)
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techniques can be used to produce separators whose ratio of vertices removed to edges cut is O( √ n) for boundeddegree planar graphs and twodimensional meshes and O(n 1/d ) for wellshaped ddimensional meshes. The heart of our analysis is an upper bound on the secondsmallest eigenvalues of the Laplacian
Convergence Of Alexandrov Spaces And Spectrum Of Laplacian
, 1998
"... . Denote by A(n) the family of compact ndimensional Alexandrov spaces with curvature \Gamma1, and k (M) the k th  eigenvalue of the Laplacian on M 2 A(n). We prove the continuity of k : A(n) ! R with respect to the GromovHausdorff topology for each k; n 2 N. 1. Introduction For n 2 N and D ..."
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Cited by 1 (0 self)
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. Denote by A(n) the family of compact ndimensional Alexandrov spaces with curvature \Gamma1, and k (M) the k th  eigenvalue of the Laplacian on M 2 A(n). We prove the continuity of k : A(n) ! R with respect to the GromovHausdorff topology for each k; n 2 N. 1. Introduction For n 2 N
The Asymptotics of the Laplacian on a Manifold With Boundary
, 1990
"... : Let P be a secondorder differential operator with leading symbol given by the metric tensor on a compact Riemannian manifold with boundary. We compute the asymptotics of the heat equation for Dirichlet, Neumann, and mixed boundary conditions. x1 Statement of results Let M m be a compact Riemann ..."
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Cited by 88 (24 self)
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Riemannian manifold with boundary @M: Let V be a smooth vector bundle over M equipped with a connection r V : Let E be an endomorphism of V: Define P = \Gamma(\Sigma i;j g ij r V i r V j +E) : C 1 (V ) ! C 1 (V ): Every second order elliptic operator on M with leading symbol given by the metric
A Continuum Approximation for the Excitations of the (1, 1, ..., 1) Interface in the Quantum Heisenberg model
, 1999
"... : It is shown that, with an appropriate scaling, the energy of lowlying excitations of the (1; 1; : : : ; 1) interface in the ddimensional quantum Heisenberg model are given by the spectrum of the d \Gamma 1dimensional Laplacian on an suitable domain. Keywords: Anisotropic Heisenberg ferromagnet, ..."
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Cited by 2 (1 self)
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: It is shown that, with an appropriate scaling, the energy of lowlying excitations of the (1; 1; : : : ; 1) interface in the ddimensional quantum Heisenberg model are given by the spectrum of the d \Gamma 1dimensional Laplacian on an suitable domain. Keywords: Anisotropic Heisenberg ferromagnet
Results 1  10
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1,789