21,581 research outputs found
Recursion relations for the general tree-level amplitudes in QCD with massive dirac fields
QCD amplitudes with many external fields have been studied for a long time.
At tree-level, the amplitudes can be obtained effectively by the BCFW recursion
relations. In this article, we extend the Britto-Cachazo-Feng-Witten (BCFW)
relations to the QCD amplitude of which the external fields are all massive or
include only one massless line. We find such amplitude can be split into two
parts and each part of the amplitude is of some correlated spin configuration
between the two shifted lines. After choosing proper momentum shift scheme, we
can show that each part is constructible directly. Hence, we can obtain a
general procedure for the amplitudes in QCD by the BCFW recursion relations. We
apply the procedure to several amplitudes as examples. We find such methods are
very efficient when there are many massive external fields in the amplitudes.Comment: Publish version, 21 pages, 5 figure
Latent Fisher Discriminant Analysis
Linear Discriminant Analysis (LDA) is a well-known method for dimensionality
reduction and classification. Previous studies have also extended the
binary-class case into multi-classes. However, many applications, such as
object detection and keyframe extraction cannot provide consistent
instance-label pairs, while LDA requires labels on instance level for training.
Thus it cannot be directly applied for semi-supervised classification problem.
In this paper, we overcome this limitation and propose a latent variable Fisher
discriminant analysis model. We relax the instance-level labeling into
bag-level, is a kind of semi-supervised (video-level labels of event type are
required for semantic frame extraction) and incorporates a data-driven prior
over the latent variables. Hence, our method combines the latent variable
inference and dimension reduction in an unified bayesian framework. We test our
method on MUSK and Corel data sets and yield competitive results compared to
the baseline approach. We also demonstrate its capacity on the challenging
TRECVID MED11 dataset for semantic keyframe extraction and conduct a
human-factors ranking-based experimental evaluation, which clearly demonstrates
our proposed method consistently extracts more semantically meaningful
keyframes than challenging baselines.Comment: 12 page
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