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Relation Algebra
, 2014
"... Tarski’s algebra of binary relations is formalised along the lines of the standard textbooks of Maddux and Schmidt and Ströhlein. This includes relationalgebraic concepts such as subidentities, vectors and a domain operation as well as various notions associated to functions. Relation algebras are ..."
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Tarski’s algebra of binary relations is formalised along the lines of the standard textbooks of Maddux and Schmidt and Ströhlein. This includes relationalgebraic concepts such as subidentities, vectors and a domain operation as well as various notions associated to functions. Relation algebras
PairDense Relation Algebras
 Transactions of the American Mathematical Society
, 1991
"... The central result of this paper is that every pairdense relation algebra is completely representable. A relation algebra is said to be pairdense if every nonzero element below the identity contains a "pair". A pair is the relation algebraic analogue of a relation of the form fha; ai ..."
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Cited by 83 (9 self)
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The central result of this paper is that every pairdense relation algebra is completely representable. A relation algebra is said to be pairdense if every nonzero element below the identity contains a "pair". A pair is the relation algebraic analogue of a relation of the form fha; ai
Relational algebras
 Reports of the Midwest Category Seminar IV, volume 137 of LNM
, 1970
"... All notation not otherwise specified in this paper is taken ..."
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All notation not otherwise specified in this paper is taken
Representation Theory of Artin Algebras
 Studies in Advanced Mathematics
, 1994
"... The representation theory of artin algebras, as we understand it today, is a relatively new area of mathematics, as most of the main developments have occurred ..."
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Cited by 657 (10 self)
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The representation theory of artin algebras, as we understand it today, is a relatively new area of mathematics, as most of the main developments have occurred
Algebraic Graph Theory
"... Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investiga ..."
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Cited by 868 (12 self)
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Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area
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
Relation Algebras of Intervals
 ARTIFICIAL INTELLIGENCE
, 1994
"... Given a representation of a relation algebra we construct relation algebras of pairs and of intervals. If the representation happens to be complete, homogeneous and fully universal then the pair and interval algebras can be constructed direct from the relation algebra. If, further, the original rel ..."
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Cited by 16 (3 self)
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Given a representation of a relation algebra we construct relation algebras of pairs and of intervals. If the representation happens to be complete, homogeneous and fully universal then the pair and interval algebras can be constructed direct from the relation algebra. If, further, the original
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...
Representations for small relation algebras
 Notre Dame Journal of Formal Logic
, 1994
"... Abstract There are eighteen isomorphism types of finite relation algebras with eight or fewer elements, and all of them are representable. We determine all the cardinalities of sets on which these algebras have representations. 1Introduction We say that a relation algebra is small if it has no more ..."
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Abstract There are eighteen isomorphism types of finite relation algebras with eight or fewer elements, and all of them are representable. We determine all the cardinalities of sets on which these algebras have representations. 1Introduction We say that a relation algebra is small if it has no more
Learning probabilistic relational models
 In IJCAI
, 1999
"... A large portion of realworld data is stored in commercial relational database systems. In contrast, most statistical learning methods work only with "flat " data representations. Thus, to apply these methods, we are forced to convert our data into a flat form, thereby losing much ..."
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Cited by 619 (31 self)
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A large portion of realworld data is stored in commercial relational database systems. In contrast, most statistical learning methods work only with "flat " data representations. Thus, to apply these methods, we are forced to convert our data into a flat form, thereby losing much
Results 1  10
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583,380