Laplacian coefficients of unicyclic graphs with the number of leaves and girth

Let $G$ be a graph of order $n$ and let $\mathcal{L}(G,\lambda)=\sum_{k=0}^n (-1)^{k}c_{k}(G)\lambda^{n-k}$ be the characteristic polynomial of its Laplacian matrix. Motivated by Ili\'{c} and Ili\'{c}'s conjecture [A. Ili\'{c}, M. Ili\'{c}, Laplacian coefficients of trees with given number of leaves or vertices of degree two, Linear Algebra and its Applications 431(2009)2195-2202.] on all extremal graphs which minimize all the Laplacian coefficients in the set $\mathcal{U}_{n,l}$ of all $n$-vertex unicyclic graphs with the number of leaves $l$, we investigate properties of the minimal elements in the partial set $(\mathcal{U}_{n,l}^g, \preceq)$ of the Laplacian coefficients, where $\mathcal{U}_{n,l}^g$ denote the set of $n$-vertex unicyclic graphs with the number of leaves $l$ and girth $g$. These results are used to disprove their conjecture. Moreover, the graphs with minimum Laplacian-like energy in $\mathcal{U}_{n,l}^g$ are also studied.Comment: 19 page, 4figure

Thermal Timescale Mass Transfer Rates in Intermediate-Mass X-ray Binaries

Thermal timescale mass transfer generally occurs in close binaries where the donor star is more massive than the accreting star. The mass transfer rates are usually estimated in terms of the Kelvin-Helmholtz timescale of the donor star. But recent investigations indicate that this method may overestimate the real mass transfer rates in accreting white dwarf or neutron star binary systems. We have systematically investigated the thermal-timescale mass transfer processes in intermediate-mass X-ray binaries, by calculating binary evolution sequences with various initial donor masses and orbital periods. From the calculated results we find that on average the mass transfer rates are lower than traditional estimates by a factor of $\sim 4$.Comment: 13 pages, 4 figures, and 2 tables, accepted for publication in A&

Neural Word Segmentation with Rich Pretraining

Neural word segmentation research has benefited from large-scale raw texts by leveraging them for pretraining character and word embeddings. On the other hand, statistical segmentation research has exploited richer sources of external information, such as punctuation, automatic segmentation and POS. We investigate the effectiveness of a range of external training sources for neural word segmentation by building a modular segmentation model, pretraining the most important submodule using rich external sources. Results show that such pretraining significantly improves the model, leading to accuracies competitive to the best methods on six benchmarks.Comment: Accepted by ACL 201

Neural Reranking for Named Entity Recognition

We propose a neural reranking system for named entity recognition (NER). The basic idea is to leverage recurrent neural network models to learn sentence-level patterns that involve named entity mentions. In particular, given an output sentence produced by a baseline NER model, we replace all entity mentions, such as \textit{Barack Obama}, into their entity types, such as \textit{PER}. The resulting sentence patterns contain direct output information, yet is less sparse without specific named entities. For example, "PER was born in LOC" can be such a pattern. LSTM and CNN structures are utilised for learning deep representations of such sentences for reranking. Results show that our system can significantly improve the NER accuracies over two different baselines, giving the best reported results on a standard benchmark.Comment: Accepted as regular paper by RANLP 201