This paper concerns the problem of network embedding (NE), whose aim is to learn low-dimensional representations for nodes in networks. Such dense vector representations offer great promises for many network analysis problems. However, existing NE approaches are still faced with challenges posed by the characteristics of complex networks in real-world applications. First, for many real-world networks associated with rich content information, previous NE methods tend to learn separated content and structure representations for each node, which requires a post-processing of combination. The empirical and simple combination strategies often make the final vector suboptimal. Second, the existing NE methods preserve the structure information by considering short and fixed neighborhood scope, such as the first- and/or the second-order proximities. However, it is hard to decide the scope of the neighborhood when facing a complex problem. To this end, we propose a novel sequence-to-sequence model based NE framework which is referred to as Self-Translation Network Embedding (STNE) model. With the sequences generated by random walks on a network, STNE learns the mapping that translates each sequence itself from the content sequence to the node sequence. On the one hand, the bi-directional LSTM encoder of STNE fuses the content and structure information seamlessly from the raw input. On the other hand, high-order proximity can be flexibly learned with the memories of LSTM to capture long-range structural information. By such self-translation from content to node, the learned hidden representations can be adopted as node embeddings. Extensive experimental results based on three real-world datasets demonstrate that the proposed STNE outperforms the state-of-the-art NE approaches. To facilitate reproduction and further study, we provide Internet access to the code and datasets\footnotehttp://dm.nankai.edu.cn/code/STNE.rar.
Finding the evolution of two level Hamiltonian is of great importance in quantum computation and quantum precision manipulation due to the requirement of quantum experiment control. However, the Schr\"odinger equation of an arbitrary time-dependent two level Hamiltonian is hardly solvable due to its non-commutativity Hamiltonian in different times. In this article, we expand and demonstrate an exact solution of Schr\"odinger equation respect to general two level systems with a few limitations. This analytical solution has lots of manipulative parameters and a few boundary restrictions, which could drive many applications. Furthermore, we show the adaptive capacity of our scheme, which demonstrated the widely use of our scheme, and make it suitable for most of experiment Hamiltonian directly.
Hashtags have always been important elements in many social network platforms and micro-blog services. Semantic understanding of hashtags is a critical and fundamental task for many applications on social networks, such as event analysis, theme discovery, information retrieval, etc. However, this task is challenging due to the sparsity, polysemy, and synonymy of hashtags. In this paper, we investigate the problem of hashtag embedding by combining the short text content with the various heterogeneous relations in social networks. Specifically, we first establish a network with hashtags as its nodes. Hierarchically, each of the hashtag nodes is associated with a set of tweets and each tweet contains a set of words. Then we devise an embedding model, called Hashtag2Vec, which exploits multiple relations of hashtag-hashtag, hashtag-tweet, tweet-word, and word-word relations based on the hierarchical heterogeneous network. In addition to embedding the hashtags, our proposed framework is capable of embedding the short social texts as well. Extensive experiments are conducted on two real-world datasets, and the results demonstrate the effectiveness of the proposed method.
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