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15,126
Decoding by Linear Programming
, 2004
"... This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector f ∈ Rn from corrupted measurements y = Af + e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to rec ..."
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Cited by 1399 (16 self)
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for some ρ> 0. In short, f can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program). In addition, numerical experiments suggest that this recovery procedure works unreasonably well; f is recovered exactly even in situations where a significant
Multiple sequence alignment with the Clustal series of programs
 Nucleic Acids Res
, 2003
"... The Clustal series of programs are widely used in molecular biology for the multiple alignment of both nucleic acid and protein sequences and for preparing phylogenetic trees. The popularity of the programs depends on a number of factors, including not only the accuracy of the results, but also the ..."
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Cited by 747 (5 self)
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the robustness, portability and userfriendliness of the programs. New features include NEXUS and FASTA format output, printing range numbers and faster tree calculation. Although, Clustal was originally developed to run on a local computer, numerous Web servers have been set up, notably at the EBI
Automatic Discovery of Linear Restraints Among Variables of a Program
, 1978
"... The model of abstract interpretation of programs developed by Cousot and Cousot [2nd ISOP, 1976], Cousot and Cousot [POPL 1977] and Cousot [PhD thesis 1978] is applied to the static determination of linear equality or inequality invariant relations among numerical variables of programs. ..."
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Cited by 726 (43 self)
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The model of abstract interpretation of programs developed by Cousot and Cousot [2nd ISOP, 1976], Cousot and Cousot [POPL 1977] and Cousot [PhD thesis 1978] is applied to the static determination of linear equality or inequality invariant relations among numerical variables of programs.
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
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Cited by 483 (2 self)
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. This paper studies a method called convex relaxation, which attempts to recover the ideal sparse signal by solving a convex program. This approach is powerful because the optimization can be completed in polynomial time with standard scientific software. The paper provides general conditions which ensure
The ensemble Kalman Filter: Theoretical formulation and practical implementation.
 Ocean Dynamics,
, 2003
"... Abstract The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group and numerous publications have discussed applications and theoretical aspects of it. This paper rev ..."
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Cited by 496 (5 self)
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numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal
Formal Numerical Program Analysis
, 1994
"... This paper describes a method for formally analyzing numerical programs and a software system that implements the method. The software system translates a purely functional PreScheme program that manipulates machine integers into a representation in the imps Interactive Mathematical Proof System. T ..."
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This paper describes a method for formally analyzing numerical programs and a software system that implements the method. The software system translates a purely functional PreScheme program that manipulates machine integers into a representation in the imps Interactive Mathematical Proof System
Exact Matrix Completion via Convex Optimization
, 2008
"... We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfe ..."
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Cited by 873 (26 self)
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perfectly recover most lowrank matrices from what appears to be an incomplete set of entries. We prove that if the number m of sampled entries obeys m ≥ C n 1.2 r log n for some positive numerical constant C, then with very high probability, most n × n matrices of rank r can be perfectly recovered
MATRIX FACTORIZATION TECHNIQUES FOR RECOMMENDER SYSTEMS
 IEEE COMPUTER
, 2009
"... As the Netflix Prize competition has demonstrated, matrix factorization models are superior to classic nearestneighbor techniques for producing product recommendations, allowing the incorporation of additional information such as implicit feedback, temporal effects, and confidence levels. Modern co ..."
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Cited by 593 (4 self)
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Amazon.com and Netflix have made recommender systems a salient part of their websites. Such systems are particularly useful for entertainment products such as movies, music, and TV shows. Many customers will view the same movie, and each customer is likely to view numerous different movies. Customers
Partial evaluation of numerical programs in Fortran
 ACM SIGPLAN WORKSHOP ON PARTIAL EVALUATION AND SEMANTICSBASED PROGRAM MANIPULATION (ORLANDO, FLORIDA)
, 1994
"... We investigate the application of partial evaluation to numerically oriented computation in scientific and engineering applications. We present our results using the Fast Fourier Transformation, the Nbody attraction problem, and the cubic splines interpolation as examples. All programs are written ..."
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Cited by 37 (1 self)
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We investigate the application of partial evaluation to numerically oriented computation in scientific and engineering applications. We present our results using the Fast Fourier Transformation, the Nbody attraction problem, and the cubic splines interpolation as examples. All programs are written
Hardwareindependent proofs of numerical programs
, 2010
"... On recent architectures, a numerical program may give different answers depending on the execution hardware and the compilation. Our goal is to formally prove properties about numerical programs that are true for multiple architectures and compilers. We propose an approach that states the rounding e ..."
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Cited by 9 (2 self)
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On recent architectures, a numerical program may give different answers depending on the execution hardware and the compilation. Our goal is to formally prove properties about numerical programs that are true for multiple architectures and compilers. We propose an approach that states the rounding
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