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Unique Minimal Liftings for Simplicial Polytopes
, 2011
"... For a minimal inequality derived from a maximal latticefree simplicial polytope in R n, we investigate the region where minimal liftings are uniquely defined, and we characterize when this region covers R n. We then use this characterization to show that a minimal inequality derived from a maximal ..."
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Cited by 6 (6 self)
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For a minimal inequality derived from a maximal latticefree simplicial polytope in R n, we investigate the region where minimal liftings are uniquely defined, and we characterize when this region covers R n. We then use this characterization to show that a minimal inequality derived from a maximal
NORMING POINTS AND UNIQUE MINIMALITY OF ORTHOGONAL PROJECTIONS
, 2005
"... We study the norming points and norming functionals of symmetric operators on Lp spaces for p = 2m or p = 2m/(2m − 1). We prove some general result relating uniqueness of minimal projection to the set of norming functionals. As a main application, we obtain that the Fourier projection onto span[1,si ..."
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We study the norming points and norming functionals of symmetric operators on Lp spaces for p = 2m or p = 2m/(2m − 1). We prove some general result relating uniqueness of minimal projection to the set of norming functionals. As a main application, we obtain that the Fourier projection onto span[1
Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ¹ minimization
 PROC. NATL ACAD. SCI. USA 100 2197–202
, 2002
"... Given a ‘dictionary’ D = {dk} of vectors dk, we seek to represent a signal S as a linear combination S = ∑ k γ(k)dk, with scalar coefficients γ(k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work considered ..."
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Cited by 626 (37 self)
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considered the special case where D is an overcomplete system consisting of exactly two orthobases, and has shown that, under a condition of mutual incoherence of the two bases, and assuming that S has a sufficiently sparse representation, this representation is unique and can be found by solving a convex
Convergent Treereweighted Message Passing for Energy Minimization
 ACCEPTED TO IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (PAMI), 2006. ABSTRACTACCEPTED TO IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (PAMI)
, 2006
"... Algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper we focus on the recent technique proposed by Wainwright et al. [33] treereweighted maxproduct message passing (TRW). It was inspired by the problem of maximizing a lower bound on the energy ..."
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Cited by 491 (16 self)
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Algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper we focus on the recent technique proposed by Wainwright et al. [33] treereweighted maxproduct message passing (TRW). It was inspired by the problem of maximizing a lower bound
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 560 (10 self)
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that for large n, and for all Φ’s except a negligible fraction, the following property holds: For every y having a representation y = Φα0 by a coefficient vector α0 ∈ R m with fewer than ρ · n nonzeros, the solution α1 of the ℓ 1 minimization problem min �x�1 subject to Φα = y is unique and equal to α0
Knots with unique minimal genus seifert surface and depth of knots
, 2003
"... We describe a procedure for creating infinite families of hyperbolic knots, each having unique minimal genus Seifert surface which cannot be the sole compact leaf of a depth one foliation. ..."
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Cited by 3 (0 self)
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We describe a procedure for creating infinite families of hyperbolic knots, each having unique minimal genus Seifert surface which cannot be the sole compact leaf of a depth one foliation.
Geodesic Active Contours
, 1997
"... A novel scheme for the detection of object boundaries is presented. The technique is based on active contours evolving in time according to intrinsic geometric measures of the image. The evolving contours naturally split and merge, allowing the simultaneous detection of several objects and both in ..."
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Cited by 1422 (47 self)
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interior and exterior boundaries. The proposed approach is based on the relation between active contours and the computation of geodesics or minimal distance curves. The minimal distance curve lays in a Riemannian space whose metric is defined by the image content. This geodesic approach for object
Applications Of Circumscription To Formalizing Common Sense Knowledge
 Artificial Intelligence
, 1986
"... We present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in (McCarthy 1980) and some applications to formalizing common sense knowledge. The applications in this paper are mostly based on minimizing the abnormality of different aspects o ..."
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Cited by 536 (12 self)
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We present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in (McCarthy 1980) and some applications to formalizing common sense knowledge. The applications in this paper are mostly based on minimizing the abnormality of different aspects
Results 1  10
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1,185,262