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Compositional Model Checking
, 1999
"... We describe a method for reducing the complexity of temporal logic model checking in systems composed of many parallel processes. The goal is to check properties of the components of a system and then deduce global properties from these local properties. The main difficulty with this type of approac ..."
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Cited by 3252 (70 self)
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component with its interface processes and then checking properties of this composition, we can guarantee that these properties will be preserved at the global level. We give two example compositional systems based on the logic CTL*.
Relations and their basic properties
 Journal of Formalized Mathematics
, 1989
"... Summary. We define here: mode Relation as a set of pairs, the domain, the codomain, and the field of relation; the empty and the identity relations, the composition of relations, the image and the inverse image of a set under a relation. Two predicates, = and ⊆, and three functions, ∪, ∩ and \ are ..."
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Cited by 1060 (6 self)
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Summary. We define here: mode Relation as a set of pairs, the domain, the codomain, and the field of relation; the empty and the identity relations, the composition of relations, the image and the inverse image of a set under a relation. Two predicates, = and ⊆, and three functions
Functions and their basic properties
 JOURNAL OF FORMALIZED MATHEMATICS
, 2003
"... The definitions of the mode Function and the graph of a function are introduced. The graph of a function is defined to be identical with the function. The following concepts are also defined: the domain of a function, the range of a function, the identity function, the composition of functions, the ..."
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Cited by 1336 (32 self)
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The definitions of the mode Function and the graph of a function are introduced. The graph of a function is defined to be identical with the function. The following concepts are also defined: the domain of a function, the range of a function, the identity function, the composition of functions
Relations defined on sets
 Journal of Formalized Mathematics
, 1989
"... Summary. The article includes theorems concerning properties of relations defined as a subset of the Cartesian product of two sets (mode Relation of X,Y where X,Y are sets). Some notions, introduced in [4] such as domain, codomain, field of a relation, composition of relations, image and inverse ima ..."
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Cited by 510 (0 self)
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Summary. The article includes theorems concerning properties of relations defined as a subset of the Cartesian product of two sets (mode Relation of X,Y where X,Y are sets). Some notions, introduced in [4] such as domain, codomain, field of a relation, composition of relations, image and inverse
Approximation by Superpositions of a Sigmoidal Function
, 1989
"... In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set ofaffine functionals can uniformly approximate any continuous function of n real variables with support in the unit hypercube; only mild conditions are imposed on the univariate fun ..."
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Cited by 1248 (2 self)
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In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set ofaffine functionals can uniformly approximate any continuous function of n real variables with support in the unit hypercube; only mild conditions are imposed on the univariate
Representing Moving Images with Layers
, 1994
"... We describe a system for representing moving images with sets of overlapping layers. Each layer contains an intensity map that defines the additive values of each pixel, along with an alpha map that serves as a mask indicating the transparency. The layers are ordered in depth and they occlude each o ..."
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Cited by 542 (11 self)
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other in accord with the rules of compositing. Velocity maps define how the layers are to be warped over time. The layered representation is more flexible than standard image transforms and can capture many important properties of natural image sequences. We describe some methods for decomposing image
A simple method for displaying the hydropathic character of a protein
 Journal of Molecular Biology
, 1982
"... A computer program that progressively evaluates the hydrophilicity and hydrophobicity of a protein along its amino acid sequence has been devised. For this purpose, a hydropathy scale has been composed wherein the hydrophilic and hydrophobic properties of each of the 20 amino acid sidechains is tak ..."
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Cited by 2287 (2 self)
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A computer program that progressively evaluates the hydrophilicity and hydrophobicity of a protein along its amino acid sequence has been devised. For this purpose, a hydropathy scale has been composed wherein the hydrophilic and hydrophobic properties of each of the 20 amino acid side
Climate and atmospheric history of the past 420,000 years from the Vostok ice core,
 Antarctica. Nature
, 1999
"... Antarctica has allowed the extension of the ice record of atmospheric composition and climate to the past four glacialinterglacial cycles. The succession of changes through each climate cycle and termination was similar, and atmospheric and climate properties oscillated between stable bounds. Inte ..."
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Cited by 716 (15 self)
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Antarctica has allowed the extension of the ice record of atmospheric composition and climate to the past four glacialinterglacial cycles. The succession of changes through each climate cycle and termination was similar, and atmospheric and climate properties oscillated between stable bounds
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24,782