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31,590
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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, ∪, ∩ and \ are redefined. Basic facts about the above mentioned notions are presented.
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 11 function, the inverse function, the restriction of a function, the image and the inverse image. Certain basic facts about functions and the notions defined in the article are proved.
Basic Properties of Real Numbers
 Journal of Formalized Mathematics
, 1989
"... this paper. A real number is an element of R ..."
Apoptosis: a Basic Biological Phenomenon with Wideranging Implications in Tissue Kinetics
 Br. J. Cancer
, 1972
"... Summary.The term apoptosis is proposed for a hitherto little recognized mechanism of controlled cell deletion, which appears to play a complementary but opposite role to mitosis in the regulation of animal cell populations. Its morphological features suggest that it is an active, inherently program ..."
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Cited by 641 (6 self)
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number of membranebound, ultrastructurally wellpreserved fragments. In the second stage these apoptotic bodies are shed from epitheliallined surfaces or are taken up by other cells, where they undergo a series of changes resembling in vitro autolysis within phagosomes, and are rapidly degraded
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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of approach is that local properties are often not preserved at the global level. We present a general framework for using additional interface processes to model the environment for a component. These interface processes are typically much simpler than the full environment of the component. By composing a
Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
, 2003
"... One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a lowdimensional manifold embedded in a highdimensional space. Drawing on the correspondenc ..."
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Cited by 1226 (15 self)
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reduction that has localitypreserving properties and a natural connection to clustering. Some potential applications and illustrative examples are discussed.
Mean shift: A robust approach toward feature space analysis
 In PAMI
, 2002
"... A general nonparametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure, the mean shift. We prove for discrete data the convergence ..."
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Cited by 2395 (37 self)
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A general nonparametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure, the mean shift. We prove for discrete data
The English Noun Phrase in its Sentential Aspect
 PH.D. DISSERTATION MIT
, 1987
"... This dissertation is a defense of the hypothesis that the noun phrase is headed by a functional element (i.e., "nonlexical" category) D, identified with the determiner. In this way, the structure of the noun phrase parallels that of the sentence, which is headed by Infl(ection), under ass ..."
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Cited by 532 (4 self)
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assumptions now standard within the GovernmentBinding (GB) framework. The central empirical problem addressed is the question of the proper analysis of the socalled "Possing" gerund in English. This construction possesses simultaneously many properties of sentences, and many properties of noun
Highly Dynamic DestinationSequenced DistanceVector Routing (DSDV) for Mobile Computers
, 1994
"... An adhoc network is the cooperative engagement of a collection of Mobile Hosts without the required intervention of any centralized Access Point. In this paper we present an innovative design for the operation of such adhoc networks. The basic idea of the design is to operate each Mobile Host as a ..."
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Cited by 2076 (8 self)
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An adhoc network is the cooperative engagement of a collection of Mobile Hosts without the required intervention of any centralized Access Point. In this paper we present an innovative design for the operation of such adhoc networks. The basic idea of the design is to operate each Mobile Host
Efficient graphbased image segmentation.
 International Journal of Computer Vision,
, 2004
"... Abstract. This paper addresses the problem of segmenting an image into regions. We define a predicate for measuring the evidence for a boundary between two regions using a graphbased representation of the image. We then develop an efficient segmentation algorithm based on this predicate, and show ..."
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Cited by 940 (1 self)
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that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties. We apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph, and illustrate the results with both real and synthetic images. The algorithm
Results 1  10
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31,590