Results 1  10
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957
An ergodic Szemer'edi theorem for commuting transformations
 J. Analyse Math
, 1979
"... The classical Poincar6 recurrence theorem asserts that under the action of a measure preserving transformation T of a finite measure space (X, ~, p.), every set A of positive measure recurs in the sense that for some n> 0,/z (T'A n A)> 0. In [1] this was extended to multiple recurrence: ..."
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Cited by 113 (2 self)
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: the transformations T, T2,..., T k have a common power satisfying /x (A n ThA n... n Tk"A)> 0 for a set A of positive measure. We also showed that this result implies Szemer6di's theorem stating that any set of integers of positive upper density contains arbitrarily long arithmetic progressions. In [2
Kernels and Regularization on Graphs
, 2003
"... We introduce a family of kernels on graphs based on the notion of regularization operators. This generalizes in a natural way the notion of regularization and Greens functions, as commonly used for real valued functions, to graphs. It turns out that di#usion kernels can be found as a special cas ..."
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Cited by 244 (11 self)
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We introduce a family of kernels on graphs based on the notion of regularization operators. This generalizes in a natural way the notion of regularization and Greens functions, as commonly used for real valued functions, to graphs. It turns out that di#usion kernels can be found as a special
Sparse Principal Component Analysis
 Journal of Computational and Graphical Statistics
, 2004
"... Principal component analysis (PCA) is widely used in data processing and dimensionality reduction. However, PCA su#ers from the fact that each principal component is a linear combination of all the original variables, thus it is often di#cult to interpret the results. We introduce a new method ca ..."
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Cited by 279 (6 self)
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Principal component analysis (PCA) is widely used in data processing and dimensionality reduction. However, PCA su#ers from the fact that each principal component is a linear combination of all the original variables, thus it is often di#cult to interpret the results. We introduce a new method
An equivalence between sparse approximation and Support Vector Machines
 A.I. Memo 1606, MIT Arti cial Intelligence Laboratory
, 1997
"... This publication can be retrieved by anonymous ftp to publications.ai.mit.edu. The pathname for this publication is: aipublications/15001999/AIM1606.ps.Z This paper shows a relationship between two di erent approximation techniques: the Support Vector Machines (SVM), proposed by V.Vapnik (1995), ..."
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Cited by 243 (7 self)
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This publication can be retrieved by anonymous ftp to publications.ai.mit.edu. The pathname for this publication is: aipublications/15001999/AIM1606.ps.Z This paper shows a relationship between two di erent approximation techniques: the Support Vector Machines (SVM), proposed by V.Vapnik (1995
Mathematical Models for Local Nontexture Inpaintings
 SIAM J. Appl. Math
, 2002
"... Inspired by the recent work of Bertalmio et al. on digital inpaintings [SIGGRAPH 2000], we develop general mathematical models for local inpaintings of nontexture images. On smooth regions, inpaintings are connected to the harmonic and biharmonic extensions, and inpainting orders are analyzed. For i ..."
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Cited by 214 (29 self)
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. For inpaintings involving the recovery of edges, we study a variational model that is closely connected to the classical total variation (TV) denoising model of Rudin, Osher, and Fatemi [PhSG D, 60 (1992), pp. 259268]. Other models are also discussed based on the MumfordShah regularity [Comm. Pure Appl. Mathq
Estimates and regularity results for the DiPernaLions flows
 J. REINE ANGEW. MATH
"... In this paper we derive new simple estimates for ordinary differential equations with Sobolev coefficients. These estimates not only allow to recover some old and recent results in a simple direct way, but they also have some new interesting corollaries. ..."
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Cited by 49 (5 self)
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In this paper we derive new simple estimates for ordinary differential equations with Sobolev coefficients. These estimates not only allow to recover some old and recent results in a simple direct way, but they also have some new interesting corollaries.
di
, 2003
"... Consistent with the theory of real options, it is argued that the value of the Employment Guarantee Scheme (EGS) in the Indian state of Maharashtra and its impact on workers ’ behaviour do not depend so much on its income supplementation as on enlargement of opportunities in an uncertain environment ..."
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of various employment options are taken into account. Finally, allowance is made for volatility of regular labour market activities (e.g. agricultural wage earnings). The predictions of this model are validated with the help of a panel household survey in a semiarid region of south India. If this analysis
Diffusion and Regularization of Vector and MatrixValued Images
, 2002
"... The goal of this paper is to present a unified description of diffusion and regularization techniques for vectorvalued as well as matrixvalued data fields. In the vectorvalued setting, we first review a number of existing methods and classify them into linear and nonlinear as well as isotropic an ..."
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Cited by 53 (16 self)
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. In this context a novel class of anisotropic di usion and regularization methods is derived and it is shown that suitable algorithmic realizations preserve the positive semidefiniteness of the matrix field without any additional constraints. As an application, we present an anisotropic nonlinear structure tensor
On graphs with linear Ramsey numbers
 J. GRAPH THEORY
, 2000
"... For a fixed graph H, the Ramsey number r (H) is defined to be the least integer N such that in any 2coloring of the edges of the complete graph KN, some monochromatic copy of H is always formed. Let H(n,) denote the class of graphs H having n vertices and maximum degree at most. It was shown by Chv ..."
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Cited by 34 (2 self)
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by ChvataÂl, Rödl, SzemereÂ di, and Trotter that for each there exists c ( ) such that r (H) < c ()n for all H 2H(n,). That is, the Ramsey numbers grow linearly with the size of H. However, their proof relied on the wellknown regularity lemma of SzemereÂ di and only gave an upper bound for c ( ) which
Regularity and compactness for the DiPerna–Lions flow
"... When b: [0, T] × Rd → Rd is a bounded smooth vector field, the flow of b is the smooth map X: [0, T] × Rd → Rd such that dX ⎪ ⎨ (t, x) = b(t, X(t, x)) , t ∈ [0, T] dt (1) X(0, x) = x. Existence and uniqueness of the flow are guaranteed by the classical Cauchy– Lipschitz theorem. The study of (1) ..."
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When b: [0, T] × Rd → Rd is a bounded smooth vector field, the flow of b is the smooth map X: [0, T] × Rd → Rd such that dX ⎪ ⎨ (t, x) = b(t, X(t, x)) , t ∈ [0, T] dt (1) X(0, x) = x. Existence and uniqueness of the flow are guaranteed by the classical Cauchy– Lipschitz theorem. The study of (1) out of the smooth context is of great importance (for instance, in view of the possible applications to conservation laws or to the theory of the motion of fluids) and has been studied by several authors. What can be said about the well–posedness of (1) when b is only in some class of weak differentiability? We remark from the beginning that no generic uniqueness results (i.e. for a.e. initial datum x) are presently available. This question can be, in some sense, “relaxed ” (and this relaxed problem
Results 1  10
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957