Component-Enhanced Chinese Character Embeddings

Distributed word representations are very useful for capturing semantic information and have been successfully applied in a variety of NLP tasks, especially on English. In this work, we innovatively develop two component-enhanced Chinese character embedding models and their bigram extensions. Distinguished from English word embeddings, our models explore the compositions of Chinese characters, which often serve as semantic indictors inherently. The evaluations on both word similarity and text classification demonstrate the effectiveness of our models.Comment: 6 pages, 2 figures, conference, EMNLP 201

The generalized 3-connectivity of Cartesian product graphs

The generalized connectivity of a graph, which was introduced recently by Chartrand et al., is a generalization of the concept of vertex connectivity. Let $S$ be a nonempty set of vertices of $G$, a collection $\{T_1,T_2,...,T_r\}$ of trees in $G$ is said to be internally disjoint trees connecting $S$ if $E(T_i)\cap E(T_j)=\emptyset$ and $V(T_i)\cap V(T_j)=S$ for any pair of distinct integers $i,j$, where $1\leq i,j\leq r$. For an integer $k$ with $2\leq k\leq n$, the $k$-connectivity $\kappa_k(G)$ of $G$ is the greatest positive integer $r$ for which $G$ contains at least $r$ internally disjoint trees connecting $S$ for any set $S$ of $k$ vertices of $G$. Obviously, $\kappa_2(G)=\kappa(G)$ is the connectivity of $G$. Sabidussi showed that $\kappa(G\Box H) \geq \kappa(G)+\kappa(H)$ for any two connected graphs $G$ and $H$. In this paper, we first study the 3-connectivity of the Cartesian product of a graph $G$ and a tree $T$, and show that $(i)$ if $\kappa_3(G)=\kappa(G)\geq 1$, then $\kappa_3(G\Box T)\geq \kappa_3(G)$; $(ii)$ if $1\leq \kappa_3(G)< \kappa(G)$, then $\kappa_3(G\Box T)\geq \kappa_3(G)+1$. Furthermore, for any two connected graphs $G$ and $H$ with $\kappa_3(G)\geq\kappa_3(H)$, if $\kappa(G)>\kappa_3(G)$, then $\kappa_3(G\Box H)\geq \kappa_3(G)+\kappa_3(H)$; if $\kappa(G)=\kappa_3(G)$, then $\kappa_3(G\Box H)\geq \kappa_3(G)+\kappa_3(H)-1$. Our result could be seen as a generalization of Sabidussi's result. Moreover, all the bounds are sharp.Comment: 17 page

A study of the high-inclination population in the Kuiper belt - II. The Twotinos

As the second part of our study, in this paper we proceed to explore the dynamics of the high-inclination Twotinos in the 1:2 Neptune mean motion resonance (NMMR). Depending on the inclination $i$, we show the existence of two critical eccentricities $e_a(i)$ and $e_c(i)$, which are lower limits of the eccentricity $e$ for the resonant angle $\sigma$ to exhibit libration and asymmetric libration, respectively. Accordingly, we have determined the libration centres $\sigma_0$ for inclined orbits, which are strongly dependent on $i$. With initial $\sigma=\sigma_0$ on a fine grid of $(e, i)$, the stability of orbits in the 1:2 NMMR is probed by 4-Gyr integrations. It is shown that symmetric librators are totally unstable for $i\ge30^{\circ}$; while stable asymmetric librators exist for $i$ up to $90^{\circ}$. We further investigate the 1:2 NMMR capture and retention of planetesimals with initial inclinations $i_0\le90^{\circ}$ in the planet migration model using a time-scale of $2\times10^7$ yr. We find that: (1) the capture efficiency of the 1:2 NMMR decreases drastically with the increase of $i_0$, and it goes to 0 when $i_0\ge60^{\circ}$; (2) the probability of discovering Twotinos with $i>25^{\circ}$, beyond observed values, is roughly estimated to be $\le0.1$ per cent; (3) more particles are captured into the leading rather than the trailing asymmetric resonance for $i_0\le10^{\circ}$, but this number difference appears to be the opposite at $i_0=20^{\circ}$ and is continuously varying for even larger $i_0$; (4) captured Twotinos residing in the trailing resonance or having $i>15^{\circ}$ are practically outside the Kozai mechanism, like currently observed samples.Comment: 13 pages, 10 figures, Accepted by MNRAS. Comments welcome