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Modular elliptic curves and Fermat’s Last Theorem
 ANNALS OF MATH
, 1995
"... When Andrew John Wiles was 10 years old, he read Eric Temple Bell’s The Last Problem and was so impressed by it that he decided that he would be the first person to prove Fermat’s Last Theorem. This theorem states that there are no nonzero integers a, b, c, n with n> 2 such that a n + b n = c n ..."
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Cited by 617 (2 self)
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When Andrew John Wiles was 10 years old, he read Eric Temple Bell’s The Last Problem and was so impressed by it that he decided that he would be the first person to prove Fermat’s Last Theorem. This theorem states that there are no nonzero integers a, b, c, n with n> 2 such that a n + b n = c
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 2401 (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 Concept of a Linguistic Variable and its Application to Approximate Reasoning
 Journal of Information Science
, 1975
"... By a linguistic variable we mean a variable whose values are words or sentences in a natural or artificial language. I:or example, Age is a linguistic variable if its values are linguistic rather than numerical, i.e., young, not young, very young, quite young, old, not very oldand not very young, et ..."
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Cited by 1427 (9 self)
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By a linguistic variable we mean a variable whose values are words or sentences in a natural or artificial language. I:or example, Age is a linguistic variable if its values are linguistic rather than numerical, i.e., young, not young, very young, quite young, old, not very oldand not very young
On the Difference between Updating a Knowledge Base and Revising it
"... this paper, we argue that no such set of postulates will be adequate for every application. In particular, we make a fundamental distinction between two kinds of modifications to a knowledge base. The first one, update, consists of bringing the knowledge base up to date when the world described by i ..."
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Cited by 471 (8 self)
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this paper, we argue that no such set of postulates will be adequate for every application. In particular, we make a fundamental distinction between two kinds of modifications to a knowledge base. The first one, update, consists of bringing the knowledge base up to date when the world described
Technological pedagogical content knowledge: A framework for integrating technology in teacher knowledge.
 Teachers College Record,
, 2006
"... Abstract This paper describes a framework for teacher knowledge for technology integration called technological pedagogical content knowledge (originally TPCK, now known as TPACK, or technology, pedagogy, and content knowledge). This framework builds on Lee Shulman's construct of pedagogical c ..."
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Cited by 416 (18 self)
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technologies present to teachers. In our work, the word technology applies equally to analog and digital, as well as new and old, technologies. As a matter of practical significance, however, most of the technologies under consideration in current literature are newer and digital and have some inherent
Visual Marking: Dissociating Effects of New and Old Set Size
 Journal of Experimental Psychology: Learning, Memory, and Cognition
, 2002
"... this article should be addressed to Yuhong Jiang, who is now at the Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, NE 20443B, Cambridge, Massachusetts 02139. Email: yuhong@mit.edu Journal of Experimental Psychology: Copyright 2002 by th ..."
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Cited by 12 (2 self)
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this article should be addressed to Yuhong Jiang, who is now at the Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, NE 20443B, Cambridge, Massachusetts 02139. Email: yuhong@mit.edu Journal of Experimental Psychology: Copyright 2002 by the American Psychological Association, Inc. Learning, Memory, and Cognition 2002, Vol. 28, No. 2, 293302 02787393/02/$5.00 DOI: 10.1037//02787393.28.2.293 293 comparable slopes and comparable overall RTs in the valid and invalid or nopreview conditions, implying no visual marking. However, measures of slope and overall RT may sometimes conflict, as when overall RT is faster in the valid preview condition compared with the invalid preview (or nopreview) condition, but the search slopes are equal (Watson & Humphreys, 1998). In the past, the lack of a difference in search rate in such a pattern of results has been taken as evidence for an absence of visual marking
CollusionSecure Fingerprinting for Digital Data
 IEEE Transactions on Information Theory
, 1996
"... This paper discusses methods for assigning codewords for the purpose of fingerprinting digital data (e.g., software, documents, and images). Fingerprinting consists of uniquely marking and registering each copy of the data. This marking allows a distributor to detect any unauthorized copy and trac ..."
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Cited by 353 (1 self)
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and trace it back to the user. This threat of detection will hopefully deter users from releasing unauthorized copies. A problem arises when users collude: For digital data, two different fingerprinted objects can be compared and the differences between them detected. Hence, a set of users can collude
Mining timechanging data streams
 IN PROC. OF THE 2001 ACM SIGKDD INTL. CONF. ON KNOWLEDGE DISCOVERY AND DATA MINING
, 2001
"... Most statistical and machinelearning algorithms assume that the data is a random sample drawn from a stationary distribution. Unfortunately, most of the large databases available for mining today violate this assumption. They were gathered over months or years, and the underlying processes genera ..."
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Cited by 337 (5 self)
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changing data streams, based on the ultrafast VFDT decision tree learner. This algorithm, called CVFDT, stays current while making the most of old data by growing an alternative subtree whenever an old one becomes questionable, and replacing the old with the new when the new becomes more accurate. CVFDT
Pragmatics of measuring recognition memory: Applications to dementia and amnesia.
 Journal of Experimental Psychology: General,
, 1988
"... SUMMARY This article has two purposes. The first is to describe four theoretical models of yesno recognition memory and present their associated measures of discrimination and response bias. These models are then applied to a set of data from normal subjects to determine which pairs of discriminati ..."
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Cited by 324 (0 self)
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SUMMARY This article has two purposes. The first is to describe four theoretical models of yesno recognition memory and present their associated measures of discrimination and response bias. These models are then applied to a set of data from normal subjects to determine which pairs
Convergence of a block coordinate descent method for nondifferentiable minimization
 J. OPTIM THEORY APPL
, 2001
"... We study the convergence properties of a (block) coordinate descent method applied to minimize a nondifferentiable (nonconvex) function f(x1,...,xN) with certain separability and regularity properties. Assuming that f is continuous on a compact level set, the subsequence convergence of the iterate ..."
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Cited by 296 (3 self)
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and compactness of the level set may be relaxed further. These results are applied to derive new (and old) convergence results for the proximal minimization algorithm, an algorithm of Arimoto and Blahut, and an algorithm of Han. They are applied also to a problem of blind source separation.
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