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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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retrieval and data mining, one is often confronted with intrinsically low dimensional data lying in a very high dimensional space. For example, gray scale n x n images of a fixed object taken with a moving camera yield data points in rn: n2 . However , the intrinsic dimensionality of the space of all images
rn
"... Abstract—The residue number system (RNS), due to its properties, is used in applications in which high performance computation is needed. The carry free nature, which makes the arithmetic, carry bounded as well as the paralleling facility is the reason of its capability of high speed rendering. Sinc ..."
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. Since carry is not propagated between the moduli in this system, the performance is only restricted by the speed of the operations in each modulus. In this paper a novel method of number representation by use of redundancy n n n is suggested in which { r �2, r �1, r} is the reference moduli set where r
The nullspaces of elliptic partial differential operators in Rn
, 1972
"... The objective of this paper is to generalize the results of Lax and Phillips [4] and Walker [ó] to include elliptic partial differential operators of all orders whose coefficients approach constant values at infinity with a certain swiftness. An example is given of an elliptic operator having an inf ..."
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Cited by 135 (1 self)
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The objective of this paper is to generalize the results of Lax and Phillips [4] and Walker [ó] to include elliptic partial differential operators of all orders whose coefficients approach constant values at infinity with a certain swiftness. An example is given of an elliptic operator having
Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps
 Proceedings of the National Academy of Sciences
, 2005
"... of contexts of data analysis, such as spectral graph theory, manifold learning, nonlinear principal components and kernel methods. We augment these approaches by showing that the diffusion distance is a key intrinsic geometric quantity linking spectral theory of the Markov process, Laplace operators ..."
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Cited by 257 (45 self)
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operators, or kernels, to the corresponding geometry and density of the data. This opens the door to the application of methods from numerical analysis and signal processing to the analysis of functions and transformations of the data. Abstract. We provide a framework for structural multiscale geometric
Regularity of the obstacle problem for a fractional power of the Laplace operator
 Comm. Pure Appl. Math
"... Given a function ϕ and s ∈ (0, 1), we will study the solutions of the following obstacle problem: • u ≥ ϕ in Rn, • (−)su ≥ 0 in Rn, • (−)su(x) = 0 for those x such that u(x)> ϕ(x), • limx →+ ∞ u(x) = 0. We show that when ϕ is C1,s or smoother, the solution u is in the space C1,α for every α & ..."
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Cited by 135 (4 self)
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Given a function ϕ and s ∈ (0, 1), we will study the solutions of the following obstacle problem: • u ≥ ϕ in Rn, • (−)su ≥ 0 in Rn, • (−)su(x) = 0 for those x such that u(x)> ϕ(x), • limx →+ ∞ u(x) = 0. We show that when ϕ is C1,s or smoother, the solution u is in the space C1,α for every α
Rn+1+ t
, 2005
"... Abstract. In this paper, the continuity for LittlewoodPaley operators and its commutator on Herz type Hardy spaces are obtained. ..."
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Abstract. In this paper, the continuity for LittlewoodPaley operators and its commutator on Herz type Hardy spaces are obtained.
Pseudodifferential Operators in Lp(Rn) Spaces∗
, 2003
"... We survey general results on the boundedness of pseudodifferential operators in Lp(Rn). We mainly consider operators with nonregular symbols which are general versions of Hörmander’s class Smρ,δ. We treat the theory in a rather classic and elementary manner. To appear in Cubo Matemática Educaciona ..."
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We survey general results on the boundedness of pseudodifferential operators in Lp(Rn). We mainly consider operators with nonregular symbols which are general versions of Hörmander’s class Smρ,δ. We treat the theory in a rather classic and elementary manner. To appear in Cubo Matemática
We consider the Schrödinger operator in Rn,
"... where the free Hamiltonian, H0: = − ∆ is a selfadjoint operator with domain the ..."
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where the free Hamiltonian, H0: = − ∆ is a selfadjoint operator with domain the
RN 4;
, 1964
"... NOTICE: When government or other drawings, specifications or other data are used for any purpose other than in connection with a definitely related government procurement operation, the U. S. Government thereby incurs no responsibility, nor any obligation whatsoever; and the fact that the Governme ..."
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NOTICE: When government or other drawings, specifications or other data are used for any purpose other than in connection with a definitely related government procurement operation, the U. S. Government thereby incurs no responsibility, nor any obligation whatsoever; and the fact that the Govern
Faster scaling algorithms for network problems
 SIAM J. COMPUT
, 1989
"... This paper presents algorithms for the assignment problem, the transportation problem, and the minimumcost flow problem of operations research. The algorithms find a minimumcost solution, yet run in time close to the bestknown bounds for the corresponding problems without costs. For example, the ..."
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Cited by 163 (5 self)
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This paper presents algorithms for the assignment problem, the transportation problem, and the minimumcost flow problem of operations research. The algorithms find a minimumcost solution, yet run in time close to the bestknown bounds for the corresponding problems without costs. For example
Results 1  10
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1,188