We deal with embedding a large scale knowledge graph composed of entities and relations into a continuous vector space. TransE is a promising method proposed recently, which is very efficient while achieving state-of-the-art predictive performance. We discuss some mapping properties of relations which should be considered in embedding, such as reflexive, one-to-many, many-to-one, and many-to-many. We note that TransE does not do well in dealing with these properties. Some complex models are capable of preserving these mapping properties but sacrifice efficiency in the process. To make a good trade-off between model capacity and efficiency, in this paper we propose TransH which models a relation as a hyperplane together with a translation operation on it. In this way, we can well preserve the above mapping properties of relations with almost the same model complexity of TransE. Additionally, as a practical knowledge graph is often far from completed, how to construct negative examples to reduce false negative labels in training is very important. Utilizing the one-to-many/many-to-one mapping property of a relation, we propose a simple trick to reduce the possibility of false negative labeling. We conduct extensive experiments on link prediction, triplet classification and fact extraction on benchmark datasets like WordNet and Freebase. Experiments show TransH delivers significant improvements over TransE on predictive accuracy with comparable capability to scale up.

Abstract. In this paper, we study the representation theory of Hopf-Ore extensions of group algebras and pointed Hopf algebras of rank one over an arbitrary field k. Let H = kG(χ, a, δ) be a Hopf-Ore extension of kG and H ′ a rank one quotient Hopf algebra of H, where k is a field, G is a group, a is a central element of G and χ is a k-valued character for G with χ(a) 1. We first show that the simple weight modules over H and H ′ are finite dimensional. Then we describe the structures of all simple weight modules over H and H ′ , and classify them. We also consider the decomposition of the tensor product of two simple weight modules over H ′ into the direct sum of indecomposable modules. Furthermore, we describe the structures of finite dimensional indecomposable weight modules over H and H ′ , and classify them. Finally, when χ(a) is a primitive n-th root of unity for some n 2, we determine all finite dimensional indecomposable projective objects in the category of weight modules over H ′ .

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There are two ways of deriving the asymptotic expansion of J ν (νa), as ν → ∞, which holds uniformly for a ≥ 0. One way starts with the Bessel equation and makes use of the turning point theory for secondorder differential equations, and the other is based on a contour integral representation and applies the theory of two coalescing saddle points. In this paper, we shall derive the same result by using the three term recurrence relation J ν+1 (x) + J ν−1 (x) = (2ν/x)J ν (x). Our approach will lead to a satisfactory development of a turning point theory for second-order linear difference equations.

The human resource management (HRM) environment in China has been undergoing significant changes due to institutional, demographic and technological changes and heightened business competition domestically and internationally. At the same time, traditional cultural values remain influential in workplace relationships and affect not only the configuration of HR practices but also the way they are perceived by the workforce. In this opening paper for the special issue on Human Resource Management in China, we highlight a few organizational phenomena and challenges to HRM in China, with implications for future research. We then outline several research directions that will reflect these changes and/or incorporate cultural values. Finally, we introduce five papers included in this special issue as exemplars to encourage more research with a focus on China but with relevance to other parts of the world.