Differential Chow Form for Projective Differential Variety

In this paper, a generic intersection theorem in projective differential algebraic geometry is presented. Precisely, the intersection of an irreducible projective differential variety of dimension d>0 and order h with a generic projective differential hyperplane is shown to be an irreducible projective differential variety of dimension d-1 and order h. Based on the generic intersection theorem, the Chow form for an irreducible projective differential variety is defined and most of the properties of the differential Chow form in affine differential case are established for its projective differential counterpart. Finally, we apply the differential Chow form to a result of linear dependence over projective varieties given by Kolchin.Comment: 17 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.

The possible BπB\pi molecular state and its radiative decay

Recently, several exotic bosons have been confirmed as multi-quark states, but there are violent disputes about their inner structures, namely if they are molecular states or tetraquarks, or even mixtures of the two structures. It would be interesting to experimentally search for non-strange four-quark states with open charm or bottom which are lighter than $\Lambda_c$ or $\Lambda_b$. Reasonable arguments indicate that they are good candidates of pure molecular states $D\pi$ or $B\pi$ because pions are the lightest boson. Both $B\pi$ and $D\pi$ bound states do not decay via strong interaction. The $B\pi$ molecule may decay into $B^*$ by radiating a photon, whereas $D\pi$ molecule can only decay via weak interaction. In this paper we explore the mass spectra of $B\pi$ molecular statesby solving the corresponding B-S equation. Then the rate of radiative decay $|\frac{3}{2},\frac{1}{2}\rangle\to B^*\gamma$ is calculated and our numerical results indicate that the processes can be measured by the future experiment. We also briefly discuss the $D\pi$ case, due to the constraint of the final state phase space, it can only decay via weak interaction.Comment: 12 pages, 3 figures, 3 table