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THREEDIMENSIONAL HYPERBOLIC GEOMETRY WITH PLANES AND PLANE PARALLELISM AS ONLY PRIMITIVE NOTIONS
"... Abstract. We show that Euclidean Mobius planes can be axiomatized in terms of circles and circletangency, and that 3dimensional hyperbolic geometry can be axiomatized in terms of planes and planeparallelism. Euclidean Mobius planes have been axiomatized in the 1950s, and a particularly simple ..."
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Abstract. We show that Euclidean Mobius planes can be axiomatized in terms of circles and circletangency, and that 3dimensional hyperbolic geometry can be axiomatized in terms of planes and planeparallelism. Euclidean Mobius planes have been axiomatized in the 1950s, and a particularly simple axiom system, in terms of points, circles, incidence I, and orthogonality? can be found in [1, III.2]. The axiom system, which will be
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
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Cited by 543 (11 self)
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to the separation of the geometrical and topological aspects of the problem and to the use of two simple but powerful primitives, a geometric predicate and an operator for manipulating the topology of the diagram. The topology is represented by a new data structure for generalized diagrams, that is, embeddings
UNIVERSALEXISTENTIAL AXIOM SYSTEMS FOR GEOMETRIES EXPRESSED WITH PIERI’S ISOSCELES TRIANGLE AS SINGLE PRIMITIVE NOTION
, 2009
"... We prove that, building upon the universalexistential orthogonalitybased axiom system for metric planes presented in [28], one can provide universalexistential axiom systems – expressed solely in terms of the ternary predicate I, with I(abc) standing for ‘ab is congruent to ac’, which Pieri has i ..."
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We prove that, building upon the universalexistential orthogonalitybased axiom system for metric planes presented in [28], one can provide universalexistential axiom systems – expressed solely in terms of the ternary predicate I, with I(abc) standing for ‘ab is congruent to ac’, which Pieri has introduced 100 years ago – for metric planes, for absolute geometry with the circle axiom, for Euclidean planes, for Euclidean geometry with the circle axiom, for Klingenberg’s generalized hyperbolic planes, for plane elementary hyperbolic geometry, as well as for all the finitedimensional versions of these geometries.
Between MDPs and SemiMDPs: A Framework for Temporal Abstraction in Reinforcement Learning
 Artificial Intelligence
, 1999
"... Learning, planning, and representing knowledge at multiple levels of temporal abstraction are key, longstanding challenges for AI. In this paper we consider how these challenges can be addressed within the mathematical framework of reinforcement learning and Markov decision processes (MDPs). We ..."
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Cited by 560 (37 self)
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extend the usual notion of action in this framework to include optionsclosedloop policies for taking action over a period of time. Examples of options include picking up an object, going to lunch, and traveling to a distant city, as well as primitive actions such as muscle twitches and joint
On the Plurality of Worlds
, 1986
"... David Lewis is one of the most influential philosophers of our age, and On the Plurality of Worlds is his magnum opus. OPW1 offers an extended development and defense of the hypothesis that there are many universes, things of the same kind as the universe in which we all live, move, and have our bei ..."
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Cited by 657 (2 self)
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the material to offer a wide range of analyses of hitherto puzzling and problematic notions. We thereby effect a theoretical unification and simplification: with a small stock of primitives, we can analyze a number of important philosophical notions with a broad range of applications. But the analyses Lewis
Fuzzy extractors: How to generate strong keys from biometrics and other noisy data. Technical Report 2003/235, Cryptology ePrint archive, http://eprint.iacr.org, 2006. Previous version appeared at EUROCRYPT 2004
 34 [DRS07] [DS05] [EHMS00] [FJ01] Yevgeniy Dodis, Leonid Reyzin, and Adam
, 2004
"... We provide formal definitions and efficient secure techniques for • turning noisy information into keys usable for any cryptographic application, and, in particular, • reliably and securely authenticating biometric data. Our techniques apply not just to biometric information, but to any keying mater ..."
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Cited by 532 (38 self)
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material that, unlike traditional cryptographic keys, is (1) not reproducible precisely and (2) not distributed uniformly. We propose two primitives: a fuzzy extractor reliably extracts nearly uniform randomness R from its input; the extraction is errortolerant in the sense that R will be the same even
The Generative Lexicon
 Computational Linguistics
, 1991
"... this paper, I will discuss four major topics relating to current research in lexical semantics: methodology, descriptive coverage, adequacy of the representation, and the computational usefulness of representations. In addressing these issues, I will discuss what I think are some of the central prob ..."
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Cited by 1320 (43 self)
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problems facing the lexical semantics community, and suggest ways of best approaching these issues. Then, I will provide a method for the decomposition of lexical categories and outline a theory of lexical semantics embodying a notion of cocompositionality and type coercion, as well as several levels
A calculus for cryptographic protocols: The spi calculus
 Information and Computation
, 1999
"... We introduce the spi calculus, an extension of the pi calculus designed for the description and analysis of cryptographic protocols. We show how to use the spi calculus, particularly for studying authentication protocols. The pi calculus (without extension) suffices for some abstract protocols; the ..."
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Cited by 919 (55 self)
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; the spi calculus enables us to consider cryptographic issues in more detail. We represent protocols as processes in the spi calculus and state their security properties in terms of coarsegrained notions of protocol equivalence.
Verb Semantics And Lexical Selection
, 1994
"... ... structure. As Levin has addressed (Levin 1985), the decomposition of verbs is proposed for the purposes of accounting for systematic semanticsyntactic correspondences. This results in a series of problems for MT systems: inflexible verb sense definitions; difficulty in handling metaphor and new ..."
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Cited by 520 (4 self)
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or simple primitives, but by a set of semantic components that are sensitive to the syntactic altern
Results 1  10
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