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Completely Representable Relation Algebras
 Bull. IGPL
, 1995
"... A boolean algebra is shown to be completely representable if and only if it is atomic whereas it is shown that the class of completely representable relation algebras is not elementary. 1 Introduction There are two types of representation in algebraic logic: ordinary and complete representations. O ..."
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Cited by 5 (4 self)
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A boolean algebra is shown to be completely representable if and only if it is atomic whereas it is shown that the class of completely representable relation algebras is not elementary. 1 Introduction There are two types of representation in algebraic logic: ordinary and complete representations
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
Complete Representations in Algebraic Logic
 JOURNAL OF SYMBOLIC LOGIC
"... A boolean algebra is shown to be completely representable if and only if it is atomic, whereas it is shown that neither the class of completely representable relation algebras nor the class of completely representable cylindric algebras of any fixed dimension (at least 3) are elementary. ..."
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Cited by 42 (12 self)
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A boolean algebra is shown to be completely representable if and only if it is atomic, whereas it is shown that neither the class of completely representable relation algebras nor the class of completely representable cylindric algebras of any fixed dimension (at least 3) are elementary.
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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regular fashion. These arise regularly in connection with extremal structures: such structures often have an unexpected degree of regularity and, because of this, often give rise to an association scheme. This in turn leads to a semisimple commutative algebra and the representation theory of this algebra
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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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
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
UCPOP: A Sound, Complete, Partial Order Planner for ADL
, 1992
"... We describe the ucpop partial order planning algorithm which handles a subset of Pednault's ADL action representation. In particular, ucpop operates with actions that have conditional effects, universally quantified preconditions and effects, and with universally quantified goals. We prove ucpo ..."
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Cited by 491 (24 self)
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ucpop is both sound and complete for this representation and describe a practical implementation that succeeds on all of Pednault's and McDermott's examples, including the infamous "Yale Stacking Problem" [McDermott 1991].
Probabilistic Visual Learning for Object Representation
, 1996
"... We present an unsupervised technique for visual learning which is based on density estimation in highdimensional spaces using an eigenspace decomposition. Two types of density estimates are derived for modeling the training data: a multivariate Gaussian (for unimodal distributions) and a Mixtureof ..."
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Cited by 705 (15 self)
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We present an unsupervised technique for visual learning which is based on density estimation in highdimensional spaces using an eigenspace decomposition. Two types of density estimates are derived for modeling the training data: a multivariate Gaussian (for unimodal distributions) and a MixtureofGaussians model (for multimodal distributions). These probability densities are then used to formulate a maximumlikelihood estimation framework for visual search and target detection for automatic object recognition and coding. Our learning technique is applied to the probabilistic visual modeling, detection, recognition, and coding of human faces and nonrigid objects such as hands.
Classification in the KLONE knowledge representation system
 COGNITIVE SCIENCE
, 1985
"... KLONE lets one define and use a class of descriptive terms called Concepts, where each Concept denotes a set of objects A subsumption relation between Concepts is defined which is related to set inclusion by way of a semantics for Concepts. This subsumption relation defines a partial order on Conce ..."
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Cited by 676 (8 self)
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KLONE lets one define and use a class of descriptive terms called Concepts, where each Concept denotes a set of objects A subsumption relation between Concepts is defined which is related to set inclusion by way of a semantics for Concepts. This subsumption relation defines a partial order
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