Universal Factorization of 3n−j(j>2)3n-j (j > 2) Symbols of the First and Second Kinds for SU(2) Group and Their Direct and Exact Calculation and Tabulation

We show that general $3n-j (n>2)$ symbols of the first kind and the second kind for the group SU(2) can be reformulated in terms of binomial coefficients. The proof is based on the graphical technique established by Yutsis, et al. and through a definition of a reduced $6-j$ symbol. The resulting $3n-j$ symbols thereby take a combinatorial form which is simply the product of two factors. The one is an integer or polynomial which is the single sum over the products of reduced $6-j$ symbols. They are in the form of summing over the products of binomial coefficients. The other is a multiplication of all the triangle relations appearing in the symbols, which can also be rewritten using binomial coefficients. The new formulation indicates that the intrinsic structure for the general recoupling coefficients is much nicer and simpler, which might serves as a bridge for the study with other fields. Along with our newly developed algorithms, this also provides a basis for a direct, exact and efficient calculation or tabulation of all the $3n-j$ symbols of the SU(2) group for all range of quantum angular momentum arguments. As an illustration, we present teh results for the $12-j$ symbols of the first kind.Comment: Add tables and reference

An Intelligent QoS Identification for Untrustworthy Web Services Via Two-phase Neural Networks

QoS identification for untrustworthy Web services is critical in QoS management in the service computing since the performance of untrustworthy Web services may result in QoS downgrade. The key issue is to intelligently learn the characteristics of trustworthy Web services from different QoS levels, then to identify the untrustworthy ones according to the characteristics of QoS metrics. As one of the intelligent identification approaches, deep neural network has emerged as a powerful technique in recent years. In this paper, we propose a novel two-phase neural network model to identify the untrustworthy Web services. In the first phase, Web services are collected from the published QoS dataset. Then, we design a feedforward neural network model to build the classifier for Web services with different QoS levels. In the second phase, we employ a probabilistic neural network (PNN) model to identify the untrustworthy Web services from each classification. The experimental results show the proposed approach has 90.5% identification ratio far higher than other competing approaches.Comment: 8 pages, 5 figure

Improving the Improved Training of Wasserstein GANs: A Consistency Term and Its Dual Effect

Despite being impactful on a variety of problems and applications, the generative adversarial nets (GANs) are remarkably difficult to train. This issue is formally analyzed by \cite{arjovsky2017towards}, who also propose an alternative direction to avoid the caveats in the minmax two-player training of GANs. The corresponding algorithm, called Wasserstein GAN (WGAN), hinges on the 1-Lipschitz continuity of the discriminator. In this paper, we propose a novel approach to enforcing the Lipschitz continuity in the training procedure of WGANs. Our approach seamlessly connects WGAN with one of the recent semi-supervised learning methods. As a result, it gives rise to not only better photo-realistic samples than the previous methods but also state-of-the-art semi-supervised learning results. In particular, our approach gives rise to the inception score of more than 5.0 with only 1,000 CIFAR-10 images and is the first that exceeds the accuracy of 90% on the CIFAR-10 dataset using only 4,000 labeled images, to the best of our knowledge.Comment: Accepted as a conference paper in International Conference on Learning Representation(ICLR). Xiang Wei and Boqing Gong contributed equally in this wor