Results 1  10
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46,205
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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as the class F of those elements whose entries obey the power decay law f  (n) ≤ C · n −1/p. We take measurements 〈f, Xk〉, k = 1,..., K, where the Xk are Ndimensional Gaussian
Factoring polynomials with rational coefficients
 MATH. ANN
, 1982
"... In this paper we present a polynomialtime algorithm to solve the following problem: given a nonzero polynomial fe Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive polynomia ..."
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Cited by 961 (11 self)
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to be factored, n = deg(f) is the degree of f, and for a polynomial ~ a ~ i with real coefficients a i. i An outline of the algorithm is as follows. First we find, for a suitable small prime number p, a padic irreducible factor h of f, to a certain precision. This is done with Berlekamp's algorithm
Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition
 in Conference Record of The TwentySeventh Asilomar Conference on Signals, Systems and Computers
, 1993
"... In this paper we describe a recursive algorithm to compute representations of functions with respect to nonorthogonal and possibly overcomplete dictionaries of elementary building blocks e.g. aiEne (wa.velet) frames. We propoeea modification to the Matching Pursuit algorithm of Mallat and Zhang (199 ..."
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Cited by 637 (1 self)
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In this paper we describe a recursive algorithm to compute representations of functions with respect to nonorthogonal and possibly overcomplete dictionaries of elementary building blocks e.g. aiEne (wa.velet) frames. We propoeea modification to the Matching Pursuit algorithm of Mallat and Zhang
DeNoising By SoftThresholding
, 1992
"... Donoho and Johnstone (1992a) proposed a method for reconstructing an unknown function f on [0; 1] from noisy data di = f(ti)+ zi, iid i =0;:::;n 1, ti = i=n, zi N(0; 1). The reconstruction fn ^ is de ned in the wavelet domain by translating all the empirical wavelet coe cients of d towards 0 by an a ..."
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Cited by 1279 (14 self)
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by an amount p 2 log(n) = p n. We prove two results about that estimator. [Smooth]: With high probability ^ fn is at least as smooth as f, in any of a wide variety of smoothness measures. [Adapt]: The estimator comes nearly as close in mean square to f as any measurable estimator can come, uniformly over
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 776 (5 self)
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Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NP
Calibrating noise to sensitivity in private data analysis
 In Proceedings of the 3rd Theory of Cryptography Conference
, 2006
"... Abstract. We continue a line of research initiated in [10, 11] on privacypreserving statistical databases. Consider a trusted server that holds a database of sensitive information. Given a query function f mapping databases to reals, the socalled true answer is the result of applying f to the datab ..."
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Cited by 649 (60 self)
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to the database. To protect privacy, the true answer is perturbed by the addition of random noise generated according to a carefully chosen distribution, and this response, the true answer plus noise, is returned to the user. Previous work focused on the case of noisy sums, in which f =P i g(xi), where xi denotes
Estimating the Support of a HighDimensional Distribution
, 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propo ..."
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Cited by 783 (29 self)
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Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We
The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 506 (2 self)
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~ (1, and then the result is classical. A simple proof appears in EnriquesChisini [E, vol. 3, chap. 3], based on analyzing the totality of coverings of p1 of degree n, with a fixed number d of ordinary branch points. This method has been extended to char. p by William Fulton [F], using specializations
Shape and motion from image streams under orthography: a factorization method
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 1992
"... Inferring scene geometry and camera motion from a stream of images is possible in principle, but is an illconditioned problem when the objects are distant with respect to their size. We have developed a factorization method that can overcome this difficulty by recovering shape and motion under orth ..."
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Cited by 1094 (38 self)
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orthography without computing depth as an intermediate step. An image stream can be represented by the 2FxP measurement matrix of the image coordinates of P points tracked through F frames. We show that under orthographic projection this matrix is of rank 3. Based on this observation, the factorization method
Virtual time and global states of distributed systems.
 Proc. Workshop on Parallel and Distributed Algorithms,
, 1989
"... Abstract A distributed system can be characterized by the fact that the global state is distributed and that a common time base does not exist. However, the notion of time is an important concept in every day life of our decentralized \ r eal world" and helps to solve problems like getting a c ..."
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Cited by 744 (5 self)
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consistent population census or determining the potential causality between events. We argue that a linearly ordered structure of time is not (always) adequate for distributed systems and propose a generalized nonstandard m o del of time which consists of vectors of clocks. These clockvectors are p
Results 1  10
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46,205