Results 1  10
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2,239
Stable Distributions, Pseudorandom Generators, Embeddings and Data Stream Computation
, 2000
"... In this paper we show several results obtained by combining the use of stable distributions with pseudorandom generators for bounded space. In particular: ffl we show how to maintain (using only O(log n=ffl 2 ) words of storage) a sketch C(p) of a point p 2 l n 1 under dynamic updates of its coo ..."
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Cited by 324 (13 self)
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coordinates, such that given sketches C(p) and C(q) one can estimate jp \Gamma qj 1 up to a factor of (1 + ffl) with large probability. This solves the main open problem of [10]. ffl we obtain another sketch function C 0 which maps l n 1 into a normed space l m 1 (as opposed to C), such that m = m
Maintaining Stream Statistics over Sliding Windows (Extended Abstract)
, 2002
"... We consider the problem of maintaining aggregates and statistics over data streams, with respect to the last N data elements seen so far. We refer to this model as the sliding window model. We consider the following basic problem: Given a stream of bits, maintain a count of the number of 1's i ..."
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Cited by 269 (9 self)
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;s in the last N elements seen from the stream. We show that using O( 1 ffl log 2 N) bits of memory, we can estimate the number of 1's to within a factor of 1 + ffl. We also give a matching lower bound of \Omega\Gamma 1 ffl log 2 N) memory bits for any deterministic or randomized algorithms. We
Hardness of Approximating the Shortest Vector Problemin High Lp Norms
, 2003
"... We show that for every ffl? 0, there is a constant p(ffl) such that for all integers p * p(ffl), it is NPhard to approximate the Shortest Vector Problem in Lp norm within factor p1\Gamma ffl under randomized reductions. For large values of p, this improves the factor 21=p \Gamma ffi hardness show ..."
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Cited by 90 (3 self)
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We show that for every ffl? 0, there is a constant p(ffl) such that for all integers p * p(ffl), it is NPhard to approximate the Shortest Vector Problem in Lp norm within factor p1\Gamma ffl under randomized reductions. For large values of p, this improves the factor 21=p \Gamma ffi hardness
The Hardness of Approximate Optima in Lattices, Codes, and Systems of Linear Equations
, 1993
"... We prove the following about the Nearest Lattice Vector Problem (in any `p norm), the Nearest Codeword Problem for binary codes, the problem of learning a halfspace in the presence of errors, and some other problems. 1. Approximating the optimum within any constant factor is NPhard. 2. If for some ..."
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Cited by 170 (7 self)
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Lattice Vector Problem in the `1 norm. Also, for some of these problems we can prove the same result as above, but for a larger factor such as 2 log 1\Gammaffl n or n ffl . Improving the factor 2 log 0:5\Gammaffl n to p dimension for either of the lattice problems would imply the hardness
An elementary proof of the JohnsonLindenstrauss Lemma
, 1999
"... The JohnsonLindenstrauss lemma shows that a set of n points in high dimensional Euclidean space can be mapped down into an O(log n=ffl 2 ) dimensional Euclidean space such that the distance between any two points changes by only a factor of (1 \Sigma ffl). In this note, we prove this lemma using ..."
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Cited by 152 (1 self)
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The JohnsonLindenstrauss lemma shows that a set of n points in high dimensional Euclidean space can be mapped down into an O(log n=ffl 2 ) dimensional Euclidean space such that the distance between any two points changes by only a factor of (1 \Sigma ffl). In this note, we prove this lemma using
THE EFFECTS OF CULTURAL BIAS: A COMPARISON OF THE WISCR AND THE WlSCffl
, 1994
"... It has been suggested that the use of standardized intelligence tests is biased against minorities. This study investigates the newly revised Wechsler Intelligence Scale for Childrenm in which Wechsler states that the new scale has eliminated biased items. Comparisons of the scores on the WISCR an ..."
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It has been suggested that the use of standardized intelligence tests is biased against minorities. This study investigates the newly revised Wechsler Intelligence Scale for Childrenm in which Wechsler states that the new scale has eliminated biased items. Comparisons of the scores on the WISCR and the WISCIII of a clinical population of sixteen African American and eighteen Caucasian males, ages ten to sixteen, revealed significant differences between the two groups on the WISCIH. The minority scores decreased predictably from the WISCR to the WISCIII, but the Caucasian scores increased rather than decreasing. The findings of this study do not support the predictions and goals of revision as stated in the manual of the WISCIII. AACKNOWLEDGEMENT All data for this study were obtained through the help and cooperation of the Ft. Worth Child Study Center and Dr. Harry Brick. Special thanks is extended to this Clinic
Global Stabilizability and Observability imply Semiglobal Stabilizability by Output Feedback
 Systems & Control Letters
, 1994
"... We show that smooth global (or even semiglobal) stabilizability and uniform complete observability are sufficient properties to guarantee semiglobal stabilizability by dynamic output feedback for continuoustime nonlinear systems. Keywords: Output feedback, Semiglobal stabilizability, Uniform co ..."
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Cited by 53 (4 self)
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(x)) \Gamma V (x)] 8x 2 A : (1) When V is continuously differentiable we have trivially : V (0) (x) = @V @x (x)f(x) : (2) ffl j \Delta j denotes the Euclidean norm. ffl A function f : A ! R+ , with A ae R p , is said to be proper on A if : lim x!@A f(x) = 1 (3) where @A denotes the boundary
On the condition number of linear least squares problems in Frobenius norm
 BIT
, 1995
"... Let A be an m \Theta n, m n full rank real matrix and b a real vector of size m. We give in this paper an explicit formula for the condition number of the Linear Least Squares Problem (LLSP) defined by : min x2IR n kAx \Gamma bk 2 : Let ff and fi two positive real numbers, we choose the weigh ..."
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Cited by 22 (12 self)
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the weighted Frobenius norm k[ffA ; fib]k F on the data and the usual Euclidean norm on the solution. A straightforward generalization of the backward error of [6] for this norm is also provided. This allow us to carry out a first order estimate of the forward error for the LLSP with this norm
A recursive algorithm for the infinity–norm fixed point problem
 Journal of Complexity
, 2003
"... 2(kb \Gamma ak1=ffl))e + 1. This upper bound has order O(dlogd2(1=ffl)e) asffl! 0. For the domain [0; 1]d with ffl! 0:5 we prove a stronger result, i.e., an upper bound on the number of function component evaluations is \Gamma d+r\Gamma 1r\Gamma 1 \Delta + 2\Gamma d+rr+1\Delta where r j dlog ..."
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Cited by 5 (2 self)
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2(kb \Gamma ak1=ffl))e + 1. This upper bound has order O(dlogd2(1=ffl)e) asffl! 0. For the domain [0; 1]d with ffl! 0:5 we prove a stronger result, i.e., an upper bound on the number of function component evaluations is \Gamma d+r\Gamma 1r\Gamma 1 \Delta + 2\Gamma d+rr+1\Delta where r j dlog
An Efficient Algorithm for Minimizing a Sum of PNorms
 SIAM Journal on Optimization
, 1997
"... We study the problem of minimizing a sum of pnorms where p is a fixed real number in the interval [1; 1]. Several practical algorithms have been proposed to solve this problem. However, none of them has a known polynomial time complexity. In this paper, we transform the problem into standard conic ..."
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Cited by 16 (2 self)
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We study the problem of minimizing a sum of pnorms where p is a fixed real number in the interval [1; 1]. Several practical algorithms have been proposed to solve this problem. However, none of them has a known polynomial time complexity. In this paper, we transform the problem into standard conic
Results 1  10
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2,239