General Trinajstić Index

In memory of the outstanding theoretical chemist Nenad Trinajstić, Furtula introduced a new distance-based molecular structure descriptor "Trinajstić index" in chemical graph theory. In this paper, we propose the general Trinajstić index, and give the calculation formula of the general Trinajstić index for double-star graphs, double brooms, Kragujevac trees, firefly graphs and wheel graphs. As an application, we calculate the general Trinajstić index for some hydrocarbons

Long-tail Relation Extraction via Knowledge Graph Embeddings and Graph Convolution Networks

We propose a distance supervised relation extraction approach for long-tailed, imbalanced data which is prevalent in real-world settings. Here, the challenge is to learn accurate "few-shot" models for classes existing at the tail of the class distribution, for which little data is available. Inspired by the rich semantic correlations between classes at the long tail and those at the head, we take advantage of the knowledge from data-rich classes at the head of the distribution to boost the performance of the data-poor classes at the tail. First, we propose to leverage implicit relational knowledge among class labels from knowledge graph embeddings and learn explicit relational knowledge using graph convolution networks. Second, we integrate that relational knowledge into relation extraction model by coarse-to-fine knowledge-aware attention mechanism. We demonstrate our results for a large-scale benchmark dataset which show that our approach significantly outperforms other baselines, especially for long-tail relations.Comment: To be published in NAACL 201

Combined Convex Technique on Delay-Distribution-Dependent Stability for Delayed Neural Networks

Together with the Lyapunov-Krasovskii functional approach and an improved delay-partitioning idea, one novel sufficient condition is derived to guarantee a class of delayed neural networks to be asymptotically stable in the mean-square sense, in which the probabilistic variable delay and both of delay variation limits can be measured. Through combining the reciprocal convex technique and convex technique one, the criterion is presented via LMIs and its solvability heavily depends on the sizes of both time-delay range and its variations, which can become much less conservative than those present ones by thinning the delay intervals. Finally, it can be demonstrated by four numerical examples that our idea reduces the conservatism more effectively than some earlier reported ones

Pinning Cluster Synchronization in Linear Hybrid Coupled Delayed Dynamical Networks

The problem on cluster synchronization will be investigated for a class of delayed dynamical networks based on pinning control strategy. Through utilizing the combined convex technique and Kronecker product, two sufficient conditions can be derived to ensure the desired synchronization when the designed feedback controller is employed to each cluster. Moreover, the inner coupling matrices are unnecessarily restricted to be diagonal and the controller design can be converted into solving a series of linear matrix inequalities (LMIs), which greatly improve the present methods. Finally, two numerical examples are provided to demonstrate the effectiveness and reduced conservatism