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Learning to Paraphrase: An Unsupervised Approach Using MultipleSequence Alignment
, 2003
"... We address the texttotext generation problem of sentencelevel paraphrasing  a phenomenon distinct from and more difficult than word or phraselevel paraphrasing. Our approach applies multiplesequence alignment to sentences gathered from unannotated comparable corpora: it learns a set of para ..."
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Cited by 258 (2 self)
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of paraphrasing patterns represented by word lattice pairs and automatically determines how to apply these patterns to rewrite new sentences. The results of our evaluation experiments show that the system derives accurate paraphrases, outperforming baseline systems.
LATTICES
, 2000
"... A formula of luminosity of asymmetric e+e collider with coupled lattices is derived explicitly. The calculation shows how the tilted angle and aspect ratio of the beams aect the luminosity. Knowing the result of the calculation, we measure the tilted angle of the luminous region of the collision fo ..."
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A formula of luminosity of asymmetric e+e collider with coupled lattices is derived explicitly. The calculation shows how the tilted angle and aspect ratio of the beams aect the luminosity. Knowing the result of the calculation, we measure the tilted angle of the luminous region of the collision
LATTICES
"... Dedicated to Jurgen Schmidt on his sixtieth birthday. In the late 1930's Birkhoff [ l] proposed the investigation of the exponent PQ of partially ordered sets P and Q, that is, the set of all orderpreserving maps of Q to P partially ordered pointwise in P. Recently, Duffus and Rival [3] have r ..."
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revitalized the efforts to settle the accompanying "cancellation law " problems. The purpose of this note is to supply a proof for the following results. THEOREM. Let L, M, and N be lattices of finite length a•d let P aud Q be finite partially ordered sets. (1) IlL P•L Q, then P•Q. (2) IlL p• M p
FCAMERGE: BottomUp Merging of Ontologies
 In IJCAI
, 2001
"... Ontologies have been established for knowledge sharing and are widely used as a means for conceptually structuring domains of interest. With the growing usage of ontologies, the problem of overlapping knowledge in a common domain becomes critical. We propose the new method FCAMERGE for mergi ..."
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Cited by 237 (9 self)
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analysis to derive a lattice of concepts as a structural result of FCAMERGE.
The Hardness of Approximate Optima in Lattices, Codes, and Systems of Linear Equations
, 1993
"... We prove the following about the Nearest Lattice Vector Problem (in any `p norm), the Nearest Codeword Problem for binary codes, the problem of learning a halfspace in the presence of errors, and some other problems. 1. Approximating the optimum within any constant factor is NPhard. 2. If for some ..."
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Cited by 170 (7 self)
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Lattice Vector Problem in the `1 norm. Also, for some of these problems we can prove the same result as above, but for a larger factor such as 2 log 1\Gammaffl n or n ffl . Improving the factor 2 log 0:5\Gammaffl n to p dimension for either of the lattice problems would imply the hardness
An Algorithmic Theory of Lattice Points in Polyhedra
, 1999
"... We discuss topics related to lattice points in rational polyhedra, including efficient enumeration of lattice points, “short” generating functions for lattice points in rational polyhedra, relations to classical and higherdimensional Dedekind sums, complexity of the Presburger arithmetic, efficien ..."
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Cited by 128 (7 self)
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We discuss topics related to lattice points in rational polyhedra, including efficient enumeration of lattice points, “short” generating functions for lattice points in rational polyhedra, relations to classical and higherdimensional Dedekind sums, complexity of the Presburger arithmetic
Local statistics of lattice dimers
, 1997
"... Abstract. We show how to compute the probability of any given local configuration in a random tiling of the plane with dominos. That is, we explicitly compute the measures of cylinder sets for the measure of maximal entropy µ on the space of tilings of the plane with dominos. We construct a measure ..."
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Cited by 97 (13 self)
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ν on the set of lozenge tilings of the plane, show that its entropy is the topological entropy, and compute explicitly the νmeasures of cylinder sets. As applications of these results, we prove that the translation action is strongly mixing for µ and ν, and compute the rate of convergence to mixing
Superresolution video reconstruction with arbitrary sampling lattices and nonzero aperture time
 IEEE Transactions on Image Processing
, 1997
"... Abstract — Printing from an NTSC source and conversion of NTSC source material to highdefinition television (HDTV) format are some of the recent applications that motivate superresolution (SR) image and video reconstruction from lowresolution (LR) and possibly blurred sources. Existing methods for ..."
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Cited by 143 (1 self)
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video sources, this paper proposes i) a complete model of video acquisition with an arbitrary input sampling lattice and a nonzero aperture time, and ii) an algorithm based on this model using the theory of projections onto convex sets to reconstruct SR still images or video from an LR time sequence
Theory of Generalized Annotated Logic Programming and its Applications
 Journal of Logic Programming
, 1992
"... Annotated logics were introduced in [43] and later studied in [5, 7, 31, 32]. In [31], annotations were extended to allow variables and functions, and it was argued that such logics can be used to provide a formal semantics for rulebased expert systems with uncertainty. In this paper we continue to ..."
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Cited by 211 (26 self)
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to investigate the power of this approach. First, we introduce a new semantics for such programs based on ideals of lattices. Subsequently, some proposals for multivalued logic programming [5, 7, 32, 47, 40, 18] as well as some formalisms for temporal reasoning [1, 3, 42] are shown to fit into this framework
Congruence lattices of lattices
"... In the early sixties, we characterized congruence lattices of universal algebras as algebraic lattices; then our interest turned to the characterization of congruence lattices of lattices. Since these lattices are distributive, we gured that this must be an easier job. After more then 35 years, we k ..."
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Cited by 34 (14 self)
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know that we were wrong. In this Appendix, we give a brief overview of the results and methods. In Section 1, we deal with nite distributive lattices; their representation as congruence lattices raises many interesting questions and needs specialized techniques. In Section 2, we discuss the general
Results 11  20
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16,671