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On the distribution of the length of the longest increasing subsequence of random permutations
 J. Amer. Math. Soc
, 1999
"... Let SN be the group of permutations of 1, 2,...,N. If π ∈ SN,wesaythat π(i1),...,π(ik) is an increasing subsequence in π if i1 <i2 <·· · <ikand π(i1) < π(i2) < ···<π(ik). Let lN (π) be the length of the longest increasing subsequence. For example, if N =5andπis the permutation 5 1 ..."
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Cited by 495 (33 self)
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Let SN be the group of permutations of 1, 2,...,N. If π ∈ SN,wesaythat π(i1),...,π(ik) is an increasing subsequence in π if i1 <i2 <·· · <ikand π(i1) < π(i2) < ···<π(ik). Let lN (π) be the length of the longest increasing subsequence. For example, if N =5andπis the permutation 5 1
Efficient dispersal of information for security, load balancing, and fault tolerance
 Journal of the ACM
, 1989
"... Abstract. An Information Dispersal Algorithm (IDA) is developed that breaks a file F of length L = ( F ( into n pieces F,, 1 5 i 5 n, each of length ( F, 1 = L/m, so that every m pieces suffice for reconstructing F. Dispersal and reconstruction are computationally efficient. The sum of the lengths ..."
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Cited by 561 (1 self)
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Abstract. An Information Dispersal Algorithm (IDA) is developed that breaks a file F of length L = ( F ( into n pieces F,, 1 5 i 5 n, each of length ( F, 1 = L/m, so that every m pieces suffice for reconstructing F. Dispersal and reconstruction are computationally efficient. The sum of the lengths
A Simple, Fast, and Accurate Algorithm to Estimate Large Phylogenies by Maximum Likelihood
, 2003
"... The increase in the number of large data sets and the complexity of current probabilistic sequence evolution models necessitates fast and reliable phylogeny reconstruction methods. We describe a new approach, based on the maximumlikelihood principle, which clearly satisfies these requirements. The ..."
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Cited by 2182 (27 self)
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. The core of this method is a simple hillclimbing algorithm that adjusts tree topology and branch lengths simultaneously. This algorithm starts from an initial tree built by a fast distancebased method and modifies this tree to improve its likelihood at each iteration. Due to this simultaneous adjustment
ATOMIC DECOMPOSITION BY BASIS PURSUIT
, 1995
"... The TimeFrequency and TimeScale communities have recently developed a large number of overcomplete waveform dictionaries  stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for d ..."
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Cited by 2728 (61 self)
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the smallest l 1 norm of coefficients among all such decompositions. We give examples exhibiting several advantages over MOF, MP and BOB, including better sparsity, and superresolution. BP has interesting relations to ideas in areas as diverse as illposed problems, in abstract harmonic analysis, total
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 1060 (1 self)
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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
New tight frames of curvelets and optimal representations of objects with piecewise C² singularities
 COMM. ON PURE AND APPL. MATH
, 2002
"... This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along C2 edges. Conceptually, the curvelet transform is a multiscale pyramid with many directions and positions at each length scale, and needleshap ..."
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Cited by 428 (21 self)
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This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along C2 edges. Conceptually, the curvelet transform is a multiscale pyramid with many directions and positions at each length scale, and needle
Flatness and defect of nonlinear systems: Introductory theory and examples
 International Journal of Control
, 1995
"... We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman’s controllability. The distance to flatness is ..."
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Cited by 346 (23 self)
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are flat. We treat two popular ones: the crane and the car with n trailers, the motion planning of which is obtained via elementary properties of planar curves. The three nonflat examples, the simple, double and variable length pendulums, are borrowed from nonlinear physics. A high frequency control
Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems.
 Math. Programming
, 1993
"... We report on improved practical algorithms for lattice basis reduction. We propose a practical floating point version of the L3algorithm of Lenstra, Lenstra, Lov'asz (1982). We present a variant of the L3 algorithm with "deep insertions" and a practical algorithm for block KorkinZ ..."
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Cited by 327 (6 self)
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We report on improved practical algorithms for lattice basis reduction. We propose a practical floating point version of the L3algorithm of Lenstra, Lenstra, Lov'asz (1982). We present a variant of the L3 algorithm with "deep insertions" and a practical algorithm for block Korkin
Groups of polynomial growth and expanding maps
 Publ. Math., Inst. Hautes Étud. Sci
, 1981
"... Consider a group F generated by Y1,.., Yk ~F Each element yeF can be represented by a word y~P~yi,P2.., yi tpt and the number IPtI+[P~[+ 9.. %'lPtl is called the length of the word. The norm][YI [ (relative to 71,..., Ye) is defined as the minimal length of the words representing Y. Notice, t ..."
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Cited by 302 (0 self)
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Consider a group F generated by Y1,.., Yk ~F Each element yeF can be represented by a word y~P~yi,P2.., yi tpt and the number IPtI+[P~[+ 9.. %'lPtl is called the length of the word. The norm][YI [ (relative to 71,..., Ye) is defined as the minimal length of the words representing Y. Notice
For a loadfree beam of length L in motion the power balance reads
, 2013
"... A geometrically exact spatial beam finite element based on the fixedpole approach M. Gaćeˇsa a, ∗ , G. Jelenić a ..."
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A geometrically exact spatial beam finite element based on the fixedpole approach M. Gaćeˇsa a, ∗ , G. Jelenić a
Results 1  10
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13,517