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Small weak epsilonnets
, 2008
"... Given a set P of points in the plane, a set of points Q is a weak εnet with respect to a family of sets S (e.g., rectangles, disks, or convex sets) if every set of S containing εP  points contains a point of Q. In this paper, we determine bounds on εS i, the smallest epsilon that can be guarante ..."
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Cited by 13 (1 self)
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Given a set P of points in the plane, a set of points Q is a weak εnet with respect to a family of sets S (e.g., rectangles, disks, or convex sets) if every set of S containing εP  points contains a point of Q. In this paper, we determine bounds on εS i, the smallest epsilon that can
Small weak epsilonnets in three dimensions
 In Proceedings of the 18th Canadian Conference on Computational Geometry
, 2006
"... We study the problem of finding small weak εnets in three dimensions and provide new upper and lower bounds on the value of ε for which a weak εnet of a given small constant size exists. The range spaces under consideration are the set of all convex sets and the set of all halfspaces in R3. 1 ..."
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Cited by 5 (0 self)
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We study the problem of finding small weak εnets in three dimensions and provide new upper and lower bounds on the value of ε for which a weak εnet of a given small constant size exists. The range spaces under consideration are the set of all convex sets and the set of all halfspaces in R3. 1
Lower bounds for weak epsilonnets and stairconvexity
 IN: PROC. 25TH ACM SYMPOS. COMPUT. GEOM. (SOCG 2009
, 2009
"... A set N ⊂ Rd is called a weak εnet (with respect to convex sets) for a finite X ⊂ Rd if N intersects every convex set C with X ∩ C  ≥ εX. For every fixed d ≥ 2 and every r ≥ 1 we construct sets X ⊂ Rd for which every weak 1 rnet has at least Ω(r logd−1 r) points; this is the first superlinear ..."
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Cited by 13 (5 self)
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A set N ⊂ Rd is called a weak εnet (with respect to convex sets) for a finite X ⊂ Rd if N intersects every convex set C with X ∩ C  ≥ εX. For every fixed d ≥ 2 and every r ≥ 1 we construct sets X ⊂ Rd for which every weak 1 rnet has at least Ω(r logd−1 r) points; this is the first
Small Weak EpsilonNets in Three Dimensions
"... We study the problem of finding small weak εnets in three dimensions and provide new upper and lower bounds on the value of ε for which a weak εnet of a given small constant size exists. The range spaces under consideration are the set of all convex sets and the set of all halfspaces in R 3. 1 ..."
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We study the problem of finding small weak εnets in three dimensions and provide new upper and lower bounds on the value of ε for which a weak εnet of a given small constant size exists. The range spaces under consideration are the set of all convex sets and the set of all halfspaces in R 3. 1
On limits of wireless communications in a fading environment when using multiple antennas
 Wireless Personal Communications
, 1998
"... Abstract. This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bitrates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multielement array (M ..."
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Cited by 2363 (14 self)
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to the baseline n = 1 case, which by Shannon’s classical formula scales as one more bit/cycle for every 3 dB of signaltonoise ratio (SNR) increase, remarkably with MEAs, the scaling is almost like n more bits/cycle for each 3 dB increase in SNR. To illustrate how great this capacity is, even for small n, take
Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
, 2004
"... Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear m ..."
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Cited by 1513 (20 self)
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law), then it is possible to reconstruct f to within very high accuracy from a small number of random measurements. typical result is as follows: we rearrange the entries of f (or its coefficients in a fixed basis) in decreasing order of magnitude f  (1) ≥ f  (2) ≥... ≥ f  (N), and define the weakℓp ball
Rho GTPases and the actin cytoskeleton
 Science
, 1998
"... The actin cytoskeleton mediates a variety of essential biological functions in all eukaryotic cells. In addition to providing a structural framework around which cell shape and polarity are defined, its dynamic properties provide the driving force for cells to move and to divide. Understanding the b ..."
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Cited by 589 (4 self)
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). As with Rho, the cytoskeletal changes induced by Rac and Cdc42 are also associated with distinct, integrinbased adhesion complexes (Fig. 1, F and H) (3). Moreover, there is significant crosstalk between GTPases of the Ras and
The ratedistortion function for source coding with side information at the decoder
 IEEE Trans. Inform. Theory
, 1976
"... AbstractLet {(X,, Y,J}r = 1 be a sequence of independent drawings of a pair of dependent random variables X, Y. Let us say that X takes values in the finite set 6. It is desired to encode the sequence {X,} in blocks of length n into a binary stream*of rate R, which can in turn be decoded as a seque ..."
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Cited by 1055 (1 self)
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the infimum is with respect to all auxiliary random variables Z (which take values in a finite set 3) that satisfy: i) Y,Z conditiofally independent given X; ii) there exists a functionf: “Y x E +.%, such that E[D(X,f(Y,Z))] 5 d. Let Rx, y(d) be the ratedistortion function which results when the encoder
Results 1  10
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5,795,883