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Proof of a conjecture on the sequence of exceptional numbers . . .
, 2009
"... We prove a conjecture that classifies exceptional numbers. This conjecture arises in two different ways, from cryptography and from coding theory. An odd integer t ≥ 3 is said to be exceptional if f(x) = xt is APN (Almost Perfect Nonlinear) over F2 code of length 2n − 1 with two zeros ω,ω t has min ..."
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Cited by 16 (3 self)
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We prove a conjecture that classifies exceptional numbers. This conjecture arises in two different ways, from cryptography and from coding theory. An odd integer t ≥ 3 is said to be exceptional if f(x) = xt is APN (Almost Perfect Nonlinear) over F2 code of length 2n − 1 with two zeros ω,ω t has
ÉTALE WILD KERNELS OF EXCEPTIONAL NUMBER FIELDS
"... Abstract. We clarify the relationship between higher étale wild kernels of a number field at the prime 2 and the Galoiscoinvariants of Tatetwisted class groups in the 2cyclotomic tower of the field. We also determine the relationship between the étale wild kernel and the group of infinitely divis ..."
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Abstract. We clarify the relationship between higher étale wild kernels of a number field at the prime 2 and the Galoiscoinvariants of Tatetwisted class groups in the 2cyclotomic tower of the field. We also determine the relationship between the étale wild kernel and the group of infinitely
A new learning algorithm for blind signal separation

, 1996
"... A new online learning algorithm which minimizes a statistical dependency among outputs is derived for blind separation of mixed signals. The dependency is measured by the average mutual information (MI) of the outputs. The source signals and the mixing matrix are unknown except for the number of ..."
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Cited by 614 (80 self)
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A new online learning algorithm which minimizes a statistical dependency among outputs is derived for blind separation of mixed signals. The dependency is measured by the average mutual information (MI) of the outputs. The source signals and the mixing matrix are unknown except for the number
An algorithm for finding best matches in logarithmic expected time
 ACM Transactions on Mathematical Software
, 1977
"... An algorithm and data structure are presented for searching a file containing N records, each described by k real valued keys, for the m closest matches or nearest neighbors to a given query record. The computation required to organize the file is proportional to kNlogN. The expected number of recor ..."
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Cited by 753 (2 self)
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An algorithm and data structure are presented for searching a file containing N records, each described by k real valued keys, for the m closest matches or nearest neighbors to a given query record. The computation required to organize the file is proportional to kNlogN. The expected number
Understanding Normal and Impaired Word Reading: Computational Principles in QuasiRegular Domains
 PSYCHOLOGICAL REVIEW
, 1996
"... We develop a connectionist approach to processing in quasiregular domains, as exemplified by English word reading. A consideration of the shortcomings of a previous implementation (Seidenberg & McClelland, 1989, Psych. Rev.) in reading nonwords leads to the development of orthographic and phono ..."
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Cited by 584 (93 self)
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and phonological representations that capture better the relevant structure among the written and spoken forms of words. In a number of simulation experiments, networks using the new representations learn to read both regular and exception words, including lowfrequency exception words, and yet are still able
Sparse Bayesian Learning and the Relevance Vector Machine
, 2001
"... This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classification tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance vect ..."
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Cited by 949 (5 self)
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functions than a comparable SVM while offering a number of additional advantages. These include the benefits of probabilistic predictions, automatic estimation of `nuisance’ parameters, and the facility to utilise arbitrary basis functions (e.g. non`Mercer’ kernels). We detail the Bayesian framework
From Few to many: Illumination cone models for face recognition under variable lighting and pose
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... We present a generative appearancebased method for recognizing human faces under variation in lighting and viewpoint. Our method exploits the fact that the set of images of an object in fixed pose, but under all possible illumination conditions, is a convex cone in the space of images. Using a smal ..."
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Cited by 745 (12 self)
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small number of training images of each face taken with different lighting directions, the shape and albedo of the face can be reconstructed. In turn, this reconstruction serves as a generative model that can be used to render—or synthesize—images of the face under novel poses and illumination
The STATEMATE Semantics of Statecharts
, 1996
"... This article describes the semantics of the language of statecharts as implenented in the STATEMATE system [Harel et al. 1990; Harel and Politi 1996]. The initial version of this semantics was developed by a team about.10 years ago. With the added experience of the users of the system it has since b ..."
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Cited by 649 (12 self)
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the report so as to make it more widely accessible, to alleviate some of the confusion about the "official semantics of the language, and to counter a number of incorrect comments made in the literature about the way statecharts have been implemented. For example, the survey [yon der Beek 1994] does
An extensive empirical study of feature selection metrics for text classification
 J. of Machine Learning Research
, 2003
"... Machine learning for text classification is the cornerstone of document categorization, news filtering, document routing, and personalization. In text domains, effective feature selection is essential to make the learning task efficient and more accurate. This paper presents an empirical comparison ..."
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Cited by 482 (15 self)
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choice for all goals except precision, for which Information Gain yielded the best result most often. This analysis also revealed, for example, that Information Gain and ChiSquared have correlated failures, and so they work poorly together. When choosing optimal pairs of metrics for each of the four
Computation of 2groups of positive classes of exceptional number fields ∗
, 801
"... of the positive divisor classes in case the number field F has exceptional dyadic places. As an application, we compute the 2rank of the wild kernel WK2(F) in K2(F). Abstract. We present an algorithm for computing the 2group Cℓ pos F des classes positives dans le cas où le corps de nombres considé ..."
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of the positive divisor classes in case the number field F has exceptional dyadic places. As an application, we compute the 2rank of the wild kernel WK2(F) in K2(F). Abstract. We present an algorithm for computing the 2group Cℓ pos F des classes positives dans le cas où le corps de nombres
Results 1  10
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2,865,937