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949
Decoding by Linear Programming
, 2004
"... This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector f ∈ Rn from corrupted measurements y = Af + e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to rec ..."
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Cited by 1399 (16 self)
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This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector f ∈ Rn from corrupted measurements y = Af + e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible
What is the Set of Images of an Object Under All Possible Lighting Conditions
 IEEE CVPR
, 1996
"... The appearance of a particular object depends on both the viewpoint from which it is observed and the light sources by which it is illuminated. If the appearance of two objects is never identical for any pose or lighting conditions, then in theory the objects can always be distinguished or recogni ..."
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Cited by 389 (25 self)
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The appearance of a particular object depends on both the viewpoint from which it is observed and the light sources by which it is illuminated. If the appearance of two objects is never identical for any pose or lighting conditions, then in theory the objects can always be distinguished
A Mathematical View of Interiorpoint Methods for Convex Optimization
 IN CONVEX OPTIMIZATION, MPS/SIAM SERIES ON OPTIMIZATION, SIAM
, 2001
"... These lecture notes aim at developing a thorough understanding of the core theory for interiorpoint methods. The overall theory continues to grow ata rapid rate but the core ideas have remained largely unchanged for several years, since Nesterov and Nemirovskii [1] published their pathbreaking, br ..."
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Cited by 271 (2 self)
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specialists and PhD students. Therein lies the justification for these lecture notes. We develop the theory in R^n although most of the theory can be developed in arbitrary real Hilbert spaces. The restriction to finite dimensions is primarily for accessibility. The notes were developed largely in conjunction with a
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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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
BSpline Signal Processing: Part ITheory
 IEEE Trans. Signal Processing
, 1993
"... This paper describes a set of efficient filtering techniques for the processing and representation of signals in terms of continuous Bspline basis functions. We first consider the problem of determining the spline coefficients for an exact signal interpolation (direct Bspline transform). The rever ..."
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Cited by 160 (31 self)
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). The reverse operation is the signal reconstruction from its spline coefficients with an optional zooming factor rn (indirect Bspline transform) . We derive general expressions for the z transforms and the equivalent continuous impulse responses of Bspline interpolators of order n. We present simple
Optimal inequalities in probability theory: A convex optimization approach
 SIAM Journal of Optimization
"... Abstract. We propose a semidefinite optimization approach to the problem of deriving tight moment inequalities for P (X ∈ S), for a set S defined by polynomial inequalities and a random vector X defined on Ω ⊆Rn that has a given collection of up to kthorder moments. In the univariate case, we provi ..."
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Cited by 110 (11 self)
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Abstract. We propose a semidefinite optimization approach to the problem of deriving tight moment inequalities for P (X ∈ S), for a set S defined by polynomial inequalities and a random vector X defined on Ω ⊆Rn that has a given collection of up to kthorder moments. In the univariate case, we
The Theory Experiment Connection: Rn Space And Inflationary Cosmology
, 2004
"... Based on a discussion of the theory experiment connection, it is proposed to tighten the connection by replacing the real and complex number basis of physical theories by sets Rn, Cn of length 2n finite binary string numbers. The form of the numbers in Rn is based on the infinite hierarchy of 2n fig ..."
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Based on a discussion of the theory experiment connection, it is proposed to tighten the connection by replacing the real and complex number basis of physical theories by sets Rn, Cn of length 2n finite binary string numbers. The form of the numbers in Rn is based on the infinite hierarchy of 2n
The RN/CFT Correspondence
, 902
"... Recently it has been shown in 0901.0931 [hepth] that the approach to extremality for the nonextremal ReissnerNordstrom black hole is not continuous. The nonextremal RN black hole splits into two spacetimes at the extremality: an extremal black hole and a disconnected AdS2 × S 2 space which has be ..."
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Recently it has been shown in 0901.0931 [hepth] that the approach to extremality for the nonextremal ReissnerNordstrom black hole is not continuous. The nonextremal RN black hole splits into two spacetimes at the extremality: an extremal black hole and a disconnected AdS2 × S 2 space which has
HARMONIC FUNCTIONS ON COMPACT SETS IN Rn
"... Abstract. For any compact set K ⊂ Rn we develop the theory of Jensen measures and subharmonic peak points, which form the set OK, to study the Dirichlet problem on K. Initially we consider the space h(K) of functions on K which can be uniformly approximated by functions harmonic in a neighborhood o ..."
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Abstract. For any compact set K ⊂ Rn we develop the theory of Jensen measures and subharmonic peak points, which form the set OK, to study the Dirichlet problem on K. Initially we consider the space h(K) of functions on K which can be uniformly approximated by functions harmonic in a neighborhood
R^n and G^nLogics
 HigherOrder Algebra, Logic, and Term Rewriting, volume 1074 of Lecture Notes in Computer Science
, 1996
"... This paper proposes a simple, settheoretic framework providing expressive typing, higherorder functions and initial models at the same time. Building upon Russell's ramified theory of types, we develop the theory of R logics, which are axiomatisable by an ordersorted equational Horn ..."
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This paper proposes a simple, settheoretic framework providing expressive typing, higherorder functions and initial models at the same time. Building upon Russell's ramified theory of types, we develop the theory of R logics, which are axiomatisable by an ordersorted equational Horn
Results 1  10
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949