Results 1  10
of
8,679
The use of the area under the ROC curve in the evaluation of machine learning algorithms
 Pattern Recognition
, 1997
"... AbstractIn this paper we investigate the use of the area under the receiver operating characteristic (ROC) curve (AUC) as a performance measure for machine learning algorithms. As a case study we evaluate six machine learning algorithms (C4.5, Multiscale Classifier, Perceptron, Multilayer Percept ..."
Abstract

Cited by 664 (3 self)
 Add to MetaCart
AbstractIn this paper we investigate the use of the area under the receiver operating characteristic (ROC) curve (AUC) as a performance measure for machine learning algorithms. As a case study we evaluate six machine learning algorithms (C4.5, Multiscale Classifier, Perceptron, Multilayer Perceptron, kNearest Neighbours, and a Quadratic Discriminant Function) on six "real world " medical diagnostics data sets. We compare and discuss the use of AUC to the more conventional overall accuracy and find that AUC exhibits a number of desirable properties when compared to overall accuracy: increased sensitivity in Analysis of Variance (ANOVA) tests; a standard error that decreased as both AUC and the number of test samples increased; decision threshold independent; and it is invariant to a priori class probabilities. The paper concludes with the recommendation that AUC be used in preference to overall accuracy for "single number " evaluation of machine
Quantising the foliation . . .
, 2001
"... As a preliminary to discussing the quantisation of the foliation in a history form of general relativity, we show how the discussion in [1] of a history version of free, scalar quantum field theory can be augmented in such a way as to include the quantisation of the unitlength, timelike vector tha ..."
Abstract
 Add to MetaCart
As a preliminary to discussing the quantisation of the foliation in a history form of general relativity, we show how the discussion in [1] of a history version of free, scalar quantum field theory can be augmented in such a way as to include the quantisation of the unitlength, timelike vector
Attacks on Copyright Marking Systems
, 1998
"... In the last few years, a large number of schemes have been proposed for hiding copyright marks and other information in digital pictures, video, audio and other multimedia objects. We describe some contenders that have appeared in the research literature and in the field; we then present a numbe ..."
Abstract

Cited by 325 (7 self)
 Add to MetaCart
In the last few years, a large number of schemes have been proposed for hiding copyright marks and other information in digital pictures, video, audio and other multimedia objects. We describe some contenders that have appeared in the research literature and in the field; we then present a number of attacks that enable the information hidden by them to be removed or otherwise rendered unusable.
An extension of the character ring of sl(3) and its quantisation
 Commun. Math. Phys
, 1999
"... We construct a commutative ring with identity which extends the ring of characters of finite dimensional representations of sl(3). It is generated by characters with values in the group ring Z [ ˜ W] of the extended affine Weyl group of ̂ sl(3)k at k ̸ ∈ Q. The ‘quantised’ version at rational level ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We construct a commutative ring with identity which extends the ring of characters of finite dimensional representations of sl(3). It is generated by characters with values in the group ring Z [ ˜ W] of the extended affine Weyl group of ̂ sl(3)k at k ̸ ∈ Q. The ‘quantised’ version at rational
RESURGENT DEFORMATION QUANTISATION
"... Abstract. We construct a version of the complex Heisenberg algebra based on the idea of endless analytic continuation. The algebra would be large enough to capture quantum effects that escape ordinary formal deformation quantisation. ..."
Abstract
 Add to MetaCart
Abstract. We construct a version of the complex Heisenberg algebra based on the idea of endless analytic continuation. The algebra would be large enough to capture quantum effects that escape ordinary formal deformation quantisation.
That Strange Procedure Called Quantisation
, 2003
"... This is a pedagogical and (almost) selfcontained introduction into the Theorem of Groenewold and van Howe, which states that a naive transcription of Dirac’s quantisation rules cannot work. Some related issues in quantisation theory are also discussed. Firstclass constrained systems a briefly desc ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
This is a pedagogical and (almost) selfcontained introduction into the Theorem of Groenewold and van Howe, which states that a naive transcription of Dirac’s quantisation rules cannot work. Some related issues in quantisation theory are also discussed. Firstclass constrained systems a briefly
Relative formality theorem and quantisation of coisotropic submanifolds
, 2005
"... We prove a relative version of Kontsevich’s formality theorem. This theorem involves a manifold M and a submanifold C and reduces to Kontsevich’s theorem if C = M. It states that the DGLA of multivector fields on an infinitesimal neighbourhood of C is L∞quasiisomorphic to the DGLA of multidifferen ..."
Abstract

Cited by 63 (10 self)
 Add to MetaCart
of multidifferential operators acting on sections of the exterior algebra of the conormal bundle. Applications to the deformation quantisation of coisotropic submanifolds are given. The proof uses a duality transformation to reduce the theorem to a version of Kontsevich’s theorem for supermanifolds, which we also
1. The new method of quantisation
, 2001
"... 1.1 THE GENESIS OF A CURVED SPACETIME It has been generally believed that QED does not allow a classical spin for the particle described. However, it has now been shown that QED permits the spin of the particle to behave like a fourvector (Bell et al. 2000a&b). This was done by mapping the Dira ..."
Abstract
 Add to MetaCart
the Dirac and photon equation into a new form, the versatile form, ( D − A) Φ = Φ M ie (1) where e is the charge on the electron. This permits the application of QED as a quantum version of General Relativity. We will study one particular sort of curved spacetime here which we will use as the building block
Results 1  10
of
8,679