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A DISCRETE EXTENSION OF THE BLASCHKE ROLLING BALL THEOREM
, 903
"... Abstract. The Rolling Ball Theorem asserts that given a convex body K ⊂ R d in Euclidean space and having a C 2smooth surface ∂K with all principal curvatures not exceeding c> 0 at all boundary points, K necessarily has the property that to each boundary point there exists a ball Br of radius r ..."
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Abstract. The Rolling Ball Theorem asserts that given a convex body K ⊂ R d in Euclidean space and having a C 2smooth surface ∂K with all principal curvatures not exceeding c> 0 at all boundary points, K necessarily has the property that to each boundary point there exists a ball Br of radius r
The Hairy Ball Theorem via Sperner’s Lemma
, 2003
"... It is well known that any continuous tangent vector field on the sphere S 2 must, at some location, be zero. This result is known as the Hairy Ball Theorem for it can be loosely interpreted as follows: It is impossible to comb all the hairs of a fuzzy ball so that: i) each hair lies tangent to the s ..."
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It is well known that any continuous tangent vector field on the sphere S 2 must, at some location, be zero. This result is known as the Hairy Ball Theorem for it can be loosely interpreted as follows: It is impossible to comb all the hairs of a fuzzy ball so that: i) each hair lies tangent
A Simple Proof of the Restricted Isometry Property for Random Matrices
 CONSTR APPROX
, 2008
"... We give a simple technique for verifying the Restricted Isometry Property (as introduced by Candès and Tao) for random matrices that underlies Compressed Sensing. Our approach has two main ingredients: (i) concentration inequalities for random inner products that have recently provided algorithmical ..."
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Cited by 631 (64 self)
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, we obtain simple and direct proofs of Kashin’s theorems on widths of finite balls in Euclidean space (and their improvements due to Gluskin) and proofs of the existence of optimal Compressed Sensing measurement matrices. In the process, we also prove that these measurements have a certain
Documents de Travail du Centre d’Economie de la Sorbonne
"... New approach of the hairy ball theorem ..."
Balanced Allocations
 SIAM Journal on Computing
, 1994
"... Suppose that we sequentially place n balls into n boxes by putting each ball into a randomly chosen box. It is well known that when we are done, the fullest box has with high probability (1 + o(1)) ln n/ ln ln n balls in it. Suppose instead that for each ball we choose two boxes at random and place ..."
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Cited by 326 (8 self)
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uniformly at random, is deleted, and one ball is added in the manner above. We discuss consequences of this and related theorems for dynamic resource allocation, hashing, and online load balancing.
Small ball probability and Dvoretzky theorem
 Israel Journal of Mathematics
, 2007
"... Large deviation estimates are by now a standard tool in Asymptotic Convex Geometry, contrary to small deviation results. In this note we present a novel application for a small deviations inequality to a problem that is related to the diameters of random sections of high dimensional convex bodies. O ..."
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Cited by 13 (1 self)
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. Our results imply an unexpected distinction between the lower and upper inclusions in Dvoretzky Theorem. 1
Small ball probability and Dvoretzky Theorem
"... Large deviation estimates are by now a standard tool in Asymptotic Convex Geometry, contrary to small deviation results. In this note we present a novel application for a small deviations inequality to a problem that is related to the diameters of random sections of high dimensional convex bodies. O ..."
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. Our results imply an unexpected distinction between the lower and upper inclusions in Dvoretzky Theorem. 1
Bounded geometries, fractals, and lowdistortion embeddings
"... The doubling constant of a metric space (X; d) is thesmallest value * such that every ball in X can be covered by * balls of half the radius. The doubling dimension of X isthen defined as dim(X) = log2 *. A metric (or sequence ofmetrics) is called doubling precisely when its doubling dimension is ..."
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Cited by 198 (40 self)
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The doubling constant of a metric space (X; d) is thesmallest value * such that every ball in X can be covered by * balls of half the radius. The doubling dimension of X isthen defined as dim(X) = log2 *. A metric (or sequence ofmetrics) is called doubling precisely when its doubling dimension
1 Introduction Affine Lines in Spheres
, 2003
"... Because of the hairy ball theorem, the only closed 2manifold that supports a lattice ..."
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Because of the hairy ball theorem, the only closed 2manifold that supports a lattice
ON EUCLIDEAN BALLS
, 2007
"... To Professor J. J. Kohn on the occasion of his seventyfifth birthday Abstract. Contrary to the well understood structure of positive harmonic functions in the unit disk, most of the properties of positive pluriharmonic functions in symmetric domains of C n, in particular the unit ball, remain myste ..."
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To Professor J. J. Kohn on the occasion of his seventyfifth birthday Abstract. Contrary to the well understood structure of positive harmonic functions in the unit disk, most of the properties of positive pluriharmonic functions in symmetric domains of C n, in particular the unit ball, remain
Results 1  10
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885