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328
Ranks of Selmer groups in an analytic family
 Trans. Amer. Math. Soc
, 2009
"... Abstract. We study the variation of the dimension of the BlochKato Selmer group of a padic Galois representation of a number field that varies in a refined family. We show that, if one restricts ourselves to representations that are, at every place dividing p, crystalline, noncritically refined, ..."
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eigenform of weight 2 of sign −1 has rank at least 1. Contents
RBF Neural Networks and Descartes' Rule of Signs
, 2002
"... We establish versions of Descartes' rule of signs for radial basis function (RBF) neural networks. These RBF rules of signs provide tight bounds for the number of zeros of univariate networks with certain parameter restrictions. Moreover, they can be used to derive tight bounds for the VapnikC ..."
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Chervonenkis (VC) dimension and pseudodimension of these networks. In particular, we show that these dimensions are no more than linear. This result contrasts with previous work showing that RBF neural networks with two and more input nodes have superlinear VC dimension. The rules give rise also to lower bounds
Descartes' Rule of Signs for Radial Basis Function Neural Networks
 Neural Computation
, 2002
"... We establish versions of Descartes' rule of signs for radial basis function (RBF) neural networks. The RBF rules of signs provide tight bounds for the number of zeros of univariate networks with certain parameter restrictions. Moreover, they can be used to infer that the VapnikChervonenkis (VC ..."
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Chervonenkis (VC) dimension and pseudodimension of these networks are no more than linear. This contrasts with previous work showing that RBF neural networks with two and more input nodes have superlinear VC dimension. The rules give rise also to lower bounds for network sizes, thus demonstrating the relevance
1ReducedDimension Multiuser Detection
"... We present a reduceddimension multiuser detector (RDMUD) structure that significantly decreases the number of required correlation branches at the receiver frontend, while still achieving performance similar to that of the conventional matchedfilter (MF) bank. RDMUD exploits the fact that the n ..."
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to determine active users and sign detection for data recovery, and the reduceddimension decisionfeedback (RDDF) detector, which combines decisionfeedback orthogonal matching pursuit for active user detection and sign detection for data recovery. We identify conditions such that error is dominated by active
Privacy Implications of Database Ranking
"... In recent years, there has been much research in the adoption of Ranked Retrieval model (in addition to the Boolean retrieval model) in structured databases, especially those in a clientserver environment (e.g., web databases). With this model, a search query returns topk tuples according to not ..."
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generally respect the privacy settings by not directly displaying private attribute values in search query answers, many of them nevertheless take into account such private attributes in the ranking function design. The conventional belief might be that tuple ranks alone are not enough to reveal
On the matched pairs sign test using bivariate ranked set sampling: an application to environmental issues
, 2008
"... The matched pairs sign test using bivariate ranked set sampling (BVRSS) is introduced and investigated. We show that this test is asymptotically more efficient than its counterpart sign test based on a bivariate simple random sample (BVSRS). The asymptotic null distribution and the efficiency of the ..."
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Cited by 1 (1 self)
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The matched pairs sign test using bivariate ranked set sampling (BVRSS) is introduced and investigated. We show that this test is asymptotically more efficient than its counterpart sign test based on a bivariate simple random sample (BVSRS). The asymptotic null distribution and the efficiency
Nonparametric Rank Test for Nonlinearity Detection
"... In this report we propose a rank test scheme to detect the potential nonlinearity in a scalar time series. Our scheme is based on the fact that, for a stationary linear stochastic process with jointly symmetric innovations, it proves that its ordinary least square (OLS) prediction error of linear au ..."
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autoregressive (AR) predictors are symmetric about zero. With this knowledge, a discriminating statistic, namely the Wilcoxon signed rank statistic, can be derived from the prediction error. The advantage of this statistic is that it has a known null distribution, thus we can perform statistical inference
An alternative approach to (the teaching of) rank and dimension Carl de Boor Preliminaries
"... While the material in this note is meant to be taught in a first course in Linear Algebra, it is written for those teaching that course (rather than those taking it). Since maps play an essential role in this material, I would assume such a course to begin with a detailed introduction to maps, to co ..."
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,...,v n] becomes (or is represented by) the m × nmatrix with columns v 1,v 2,...,v n.Thus,V ∈ IF m×n, and the action of V on some c ∈ IF n can be described by (Vc)i = ∑ v k i ck = ∑ V (i, k)ck, all i.
Adaptation, performance and vapnikchervonenkis dimension of straight line programs
 In EuroGP
, 2009
"... Abstract. We discuss here empirical comparation between model selection methods based on Linear Genetic Programming. Two statistical methods are compared: model selection based on Empirical Risk Minimization (ERM) and model selection based on Structural Risk Minimization (SRM). For this purpose we h ..."
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Cited by 3 (3 self)
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have identified the main components which determine the capacity of some linear structures as classifiers showing an upper bound for the VapnikChervonenkis (VC) dimension of classes of programs representing linear code defined by arithmetic computations and sign tests. This upper bound is used
VapnikChervonenkis Dimension and (Pseudo)Hyperplane Arrangements
, 1993
"... An arrangement of oriented pseudohyperplanes in Euclidean dspace denes on the set X of pseudohyperplanes a set system or range space XR R X of VC dimension d in a natural way to every cell c in the arrangement assign the subset of pseudohyperplanes having c on their positive side and let R be th ..."
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Cited by 6 (1 self)
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An arrangement of oriented pseudohyperplanes in Euclidean dspace denes on the set X of pseudohyperplanes a set system or range space XR R X of VC dimension d in a natural way to every cell c in the arrangement assign the subset of pseudohyperplanes having c on their positive side and let R
Results 11  20
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328