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ON THE NUMBER OF LINEAR FORMS IN LOGARITHMS
, 2008
"... Abstract. Let n be a positive integer. In this paper we estimate the size of the set of linear forms b1 log a1 + b2 log a2 +... + bn log an, where bi  ≤ Bi and 1 ≤ ai ≤ Ai are integers, as ..."
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Abstract. Let n be a positive integer. In this paper we estimate the size of the set of linear forms b1 log a1 + b2 log a2 +... + bn log an, where bi  ≤ Bi and 1 ≤ ai ≤ Ai are integers, as
Maximum Likelihood Linear Transformations for HMMBased Speech Recognition
 COMPUTER SPEECH AND LANGUAGE
, 1998
"... This paper examines the application of linear transformations for speaker and environmental adaptation in an HMMbased speech recognition system. In particular, transformations that are trained in a maximum likelihood sense on adaptation data are investigated. Other than in the form of a simple bias ..."
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Cited by 546 (66 self)
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This paper examines the application of linear transformations for speaker and environmental adaptation in an HMMbased speech recognition system. In particular, transformations that are trained in a maximum likelihood sense on adaptation data are investigated. Other than in the form of a simple
SUMS OF SQUARES OF LINEAR FORMS
"... Abstract. Let k be a real field. We show that every nonnegative homogeneous quadratic polynomial f(x1,..., xn) with coefficients in the polynomial ring k[t] is a sum of 2n · τ(k) squares of linear forms, where τ(k) is the supremum of the levels of the finite nonreal field extensions of k. From th ..."
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Abstract. Let k be a real field. We show that every nonnegative homogeneous quadratic polynomial f(x1,..., xn) with coefficients in the polynomial ring k[t] is a sum of 2n · τ(k) squares of linear forms, where τ(k) is the supremum of the levels of the finite nonreal field extensions of k. From
Efficiently computing static single assignment form and the control dependence graph
 ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS
, 1991
"... In optimizing compilers, data structure choices directly influence the power and efficiency of practical program optimization. A poor choice of data structure can inhibit optimization or slow compilation to the point that advanced optimization features become undesirable. Recently, static single ass ..."
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Cited by 994 (8 self)
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assignment form and the control dependence graph have been proposed to represent data flow and control flow propertiee of programs. Each of these previously unrelated techniques lends efficiency and power to a useful class of program optimization. Although both of these structures are attractive
LINEAR FORM OF CANONICAL GRAVITY
, 1995
"... Summary. Recent work in the literature has shown that general relativity can be formulated in terms of a jet bundle which, in local coordinates, has five entries: local coordinates on Lorentzian spacetime, tetrads, connection oneforms, multivelocities corresponding to the tetrads and multivelocit ..."
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and multivelocities corresponding to the connection oneforms. The derivatives of the Lagrangian with respect to the latter class of multivelocities give rise to a set of multimomenta which naturally occur in the constraint equations. Interestingly, all the constraint equations of general relativity are linear
Dictionary of protein secondary structure: pattern recognition of hydrogenbonded and geometrical features
, 1983
"... For a successful analysis of the relation between amino acid sequence and protein structure, an unambiguous and physically meaningful definition of secondary structure is essential. We have developed a set of simple and physically motivated criteria for secondary structure, programmed as a patternr ..."
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Cited by 2061 (4 self)
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. ” Solvent “exposure ” is given as the number of water molecules in possible contact with a residue. The end result is a compilation of the primary structure, including SS bonds, secondary structure, and solvent exposure of 62 different globular proteins. The presentation is in linear form: strip graphs
A New Extension of the Kalman Filter to Nonlinear Systems
, 1997
"... The Kalman filter(KF) is one of the most widely used methods for tracking and estimation due to its simplicity, optimality, tractability and robustness. However, the application of the KF to nonlinear systems can be difficult. The most common approach is to use the Extended Kalman Filter (EKF) which ..."
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Cited by 747 (6 self)
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) which simply linearises all nonlinear models so that the traditional linear Kalman filter can be applied. Although the EKF (in its many forms) is a widely used filtering strategy, over thirty years of experience with it has led to a general consensus within the tracking and control community
Sparse coding with an overcomplete basis set: a strategy employed by V1
 Vision Research
, 1997
"... The spatial receptive fields of simple cells in mammalian striate cortex have been reasonably well described physiologically and can be characterized as being localized, oriented, and ban@ass, comparable with the basis functions of wavelet transforms. Previously, we have shown that these receptive f ..."
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Cited by 942 (9 self)
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for representing a given input, and so the inputoutput function will deviate from being purely linear. These deviations from linearity provide a potential explanation for the weak forms of nonlinearity observed in the response properties of cortical simple cells, and they further make predictions about
Mixtures of Probabilistic Principal Component Analysers
, 1998
"... Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a com ..."
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Cited by 526 (6 self)
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Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a
Bagging predictors
, 1996
"... Bagging predictors is a method for generating multiple versions of a predictor and using these to get an aggregated predictor. The aggregation averages over the versions when predicting a numerical outcome and does a plurality vote when predicting a class. The multiple versions are formed by making ..."
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Cited by 3564 (1 self)
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Bagging predictors is a method for generating multiple versions of a predictor and using these to get an aggregated predictor. The aggregation averages over the versions when predicting a numerical outcome and does a plurality vote when predicting a class. The multiple versions are formed
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