Analytic smoothness effect of solutions for spatially homogeneous Landau equation

In this paper, we study the smoothness effect of Cauchy problem for the spatially homogeneous Landau equation in the hard potential case and the Maxwellian molecules case. We obtain the analytic smoothing effect for the solutions under rather weak assumptions on the initial datum.Comment: 16 page

Generating Aspect-oriented Multi-document Summarization with Event-Aspect Model

In this paper, we propose a novel approach to automatic generation of aspect-oriented summaries from multiple documents. We first develop an event-aspect LDA model to cluster sentences into aspects. We then use extended LexRank algorithm to rank the sentences in each cluster. We use Integer Linear Programming for sentence selection. Key features of our method include automatic grouping of semantically related sentences and sentence ranking based on extension of random walk model. Also, we implement a new sentence compression algorithm which use dependency tree instead of parser tree. We compare our method with four baseline methods. Quantitative evaluation based on Rouge metric demonstrates the effectiveness and advantages of our method.