In this paper I study a variant of the general vertex coloring problem called precoloring. Specifically, I study graph precolorings, by developing new theory, for characterizing the minimal non-extensible precolorings. It is interesting per se that, for graphs of arbitrarily large chromatic number, the minimal number of colored vertices, in a nonextensible precoloring, remains constant; only tw...

We propose a method for implicit discourse relation recognition using a recursive neural network (RNN). Many previous studies have used the word-pair feature to compare the meaning of two sentences for implicit discourse relation recognition. Our proposed method differs in that we use various-sized sentence expression units and compare the meaning of the expressions between two sentences by con...

The purpose of this paper is to introduce a nonlinear scalarisation function for solving a class of implicit vector equilibrium problems. We prove a scalarisation lemma to show the relation between the implicit vector equilibrium problem and the nonlinear scalarisation function. Then we derive some new existence theorems for solutions of implicit vector equilibrium problems, using the scalarisa...

We provide a systematic study of previously proposed features for implicit discourse relation identification, identifying new feature combinations that optimize F1-score. The resulting classifiers achieve the best F1-scores to date for the four top-level discourse relation classes of the Penn Discourse Tree Bank: COMPARISON, CONTINGENCY, EXPANSION, and TEMPORAL. We further identify factors for ...

Implicit discourse relation recognition remains a serious challenge due to the absence of discourse connectives. In this paper, we propose a Shallow Convolutional Neural Network (SCNN) for implicit discourse relation recognition, which contains only one hidden layer but is effective in relation recognition. The shallow structure alleviates the overfitting problem, while the convolution and nonl...