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423,782
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 557 (12 self)
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mechanical way to algorithms for SDP with proofs of convergence and polynomial time complexity also carrying over in a similar fashion. Finally we study the significance of these results in a variety of combinatorial optimization problems including the general 01 integer programs, the maximum clique
Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 529 (3 self)
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Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual
A calculus of mobile processes, I
, 1992
"... We present the acalculus, a calculus of communicating systems in which one can naturally express processes which have changing structure. Not only may the component agents of a system be arbitrarily linked, but a communication between neighbours may carry information which changes that linkage. The ..."
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Cited by 1183 (31 self)
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calculus of higherorder functions (the Icalculus and combinatory algebra), the transmission of processes as values, and the representation of data structures as processes. The paper continues by presenting the algebraic theory of strong bisimilarity and strong equivalence, including a new notion of equivalence
An Extended Set of Fortran Basic Linear Algebra Subprograms
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1986
"... This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers. ..."
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Cited by 526 (72 self)
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This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers.
Using Linear Algebra for Intelligent Information Retrieval
 SIAM REVIEW
, 1995
"... Currently, most approaches to retrieving textual materials from scientific databases depend on a lexical match between words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity in the words people use to describe the same document, lexical ..."
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Cited by 672 (18 self)
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Currently, most approaches to retrieving textual materials from scientific databases depend on a lexical match between words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity in the words people use to describe the same document, lexical methods are necessarily incomplete and imprecise. Using the singular value decomposition (SVD), one can take advantage of the implicit higherorder structure in the association of terms with documents by determining the SVD of large sparse term by document matrices. Terms and documents represented by 200300 of the largest singular vectors are then matched against user queries. We call this retrieval method Latent Semantic Indexing (LSI) because the subspace represents important associative relationships between terms and documents that are not evident in individual documents. LSI is a completely automatic yet intelligent indexing method, widely applicable, and a promising way to improve users...
Qualitative process theory
 MIT AI Lab Memo
, 1982
"... Objects move, collide, flow, bend, heat up, cool down, stretch, compress. and boil. These and other things that cause changes in objects over time are intuitively characterized as processes. To understand commonsense physical reasoning and make programs that interact with the physical world as well ..."
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Cited by 884 (92 self)
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Objects move, collide, flow, bend, heat up, cool down, stretch, compress. and boil. These and other things that cause changes in objects over time are intuitively characterized as processes. To understand commonsense physical reasoning and make programs that interact with the physical world as well
A theory of communicating sequential processes
, 1984
"... A mathematical model for communicating sequential processes is given, and a number of its interesting and useful properties are stated and proved. The possibilities of nondetermimsm are fully taken into account. ..."
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Cited by 4135 (17 self)
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A mathematical model for communicating sequential processes is given, and a number of its interesting and useful properties are stated and proved. The possibilities of nondetermimsm are fully taken into account.
The eyes have it: A task by data type taxonomy for information visualizations
 IN IEEE SYMPOSIUM ON VISUAL LANGUAGES
, 1996
"... A useful starting point for designing advanced graphical user interjaces is the Visual lnformationSeeking Mantra: overview first, zoom and filter, then details on demand. But this is only a starting point in trying to understand the rich and varied set of information visualizations that have been ..."
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Cited by 1250 (28 self)
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proposed in recent years. This paper offers a task by data type taxonomy with seven data types (one, two, threedimensional datu, temporal and multidimensional data, and tree and network data) and seven tasks (overview, Zoom, filter, detailsondemand, relate, history, and extracts).
Pig Latin: A NotSoForeign Language for Data Processing
"... There is a growing need for adhoc analysis of extremely large data sets, especially at internet companies where innovation critically depends on being able to analyze terabytes of data collected every day. Parallel database products, e.g., Teradata, offer a solution, but are usually prohibitively e ..."
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Cited by 584 (12 self)
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There is a growing need for adhoc analysis of extremely large data sets, especially at internet companies where innovation critically depends on being able to analyze terabytes of data collected every day. Parallel database products, e.g., Teradata, offer a solution, but are usually prohibitively expensive at this scale. Besides, many of the people who analyze this data are entrenched procedural programmers, who find the declarative, SQL style to be unnatural. The success of the more procedural mapreduce programming model, and its associated scalable implementations on commodity hardware, is evidence of the above. However, the mapreduce paradigm is too lowlevel and rigid, and leads to a great deal of custom user code that is hard to maintain, and reuse. We describe a new language called Pig Latin that we have designed to fit in a sweet spot between the declarative style of SQL, and the lowlevel, procedural style of mapreduce. The accompanying system, Pig, is fully implemented, and compiles Pig Latin into physical plans that are executed over Hadoop, an opensource, mapreduce implementation. We give a few examples of how engineers at Yahoo! are using Pig to dramatically reduce the time required for the development and execution of their data analysis tasks, compared to using Hadoop directly. We also report on a novel debugging environment that comes integrated with Pig, that can lead to even higher productivity gains. Pig is an opensource, Apacheincubator project, and available for general use. 1.
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