On Hopf algebras of dimension 4p

Some progress on classification problems for finite dimensional Hopf algebras has been made recently. In this thesis, we look at 4p-dimensional Hopf algebras over an algebraically closed field of characteristic zero. We show that a non-semisimple Hopf algebra of dimension 4p with an odd prime p is pointed if, and only if, this Hopf algebra contains more than two group-like elements. Moreover, we prove that non-semisimple Hopf algebras of dimensions 20, 28 and 44 are either pointed or dual-pointed, and this completes the classification of Hopf algebras of dimension 20, 28,and 44

Taiwan’s Campaign for United Nations Participation

From introduction: "In terms of population, territory, govemment, foreign relations, economic development, and democratization, and under international law, Taiwan has every right to become a member of the United Nations. Since 1993, Taipei has indicated its desire and taken the appropriate actions to join the United Nations, but Beijing has consistently blocked the campaign. After President George W. Bush was inaugurated in January 2001, Taipei was able to improve relations with the United States and gained more support for joining such international organizations as the World Health Organization (WHO). Furthermore, the Ministry of Foreign Affairs (MOFA) initiated several reforms and broadened the traditional concept of diplomacy."(...

An interactively recurrent functional neural fuzzy network with fuzzy differential evolution and its applications

In this paper, an interactively recurrent functional neural fuzzy network (IRFNFN) with fuzzy differential evolution (FDE) learning method was proposed for solving the control and the prediction problems. The traditional differential evolution (DE) method easily gets trapped in a local optimum during the learning process, but the proposed fuzzy differential evolution algorithm can overcome this shortcoming. Through the information sharing of nodes in the interactive layer, the proposed IRFNFN can effectively reduce the number of required rule nodes and improve the overall performance of the network. Finally, the IRFNFN model and associated FDE learning algorithm were applied to the control system of the water bath temperature and the forecast of the sunspot number. The experimental results demonstrate the effectiveness of the proposed method

Personalized Acoustic Modeling by Weakly Supervised Multi-Task Deep Learning using Acoustic Tokens Discovered from Unlabeled Data

It is well known that recognizers personalized to each user are much more effective than user-independent recognizers. With the popularity of smartphones today, although it is not difficult to collect a large set of audio data for each user, it is difficult to transcribe it. However, it is now possible to automatically discover acoustic tokens from unlabeled personal data in an unsupervised way. We therefore propose a multi-task deep learning framework called a phoneme-token deep neural network (PTDNN), jointly trained from unsupervised acoustic tokens discovered from unlabeled data and very limited transcribed data for personalized acoustic modeling. We term this scenario "weakly supervised". The underlying intuition is that the high degree of similarity between the HMM states of acoustic token models and phoneme models may help them learn from each other in this multi-task learning framework. Initial experiments performed over a personalized audio data set recorded from Facebook posts demonstrated that very good improvements can be achieved in both frame accuracy and word accuracy over popularly-considered baselines such as fDLR, speaker code and lightly supervised adaptation. This approach complements existing speaker adaptation approaches and can be used jointly with such techniques to yield improved results.Comment: 5 pages, 5 figures, published in IEEE ICASSP 201