SL(2,C) gravity on noncommutative space with Poisson structure

The Einstein's gravity theory can be formulated as an SL(2,C) gauge theory in terms of spinor notations. In this paper, we consider a noncommutative space with the Poisson structure and construct an SL(2,C) formulation of gravity on such a space. Using the covariant coordinate technique, we build a gauge invariant action in which, according to the Seiberg-Witten map, the physical degrees of freedom are expressed in terms of their commutative counterparts up to the first order in noncommutative parameters.Comment: 12 pages, no figures; v2: 13 pages, clarifications and references added; v3: clarifications added; v4: more clarifications and references added, final version to appear in Phys. Rev.

Making a Better Query: Find Good Feedback Documents and Terms via Semantic Associations

When people search, they always input several keywords as an input query. While current information retrieval (IR) systems are based on term matching, documents will not be considered as relevant if they do not have the exact terms as in the query. However, it is common that these documents are relevant if they contain terms semantically similar to the query. To retrieve these documents, a classic way is to expand the original query with more related terms. Pseudo relevance feedback (PRF) has proven to be effective to expand origin queries and improve the performance of IR. It assumes the top k ranked documents obtained through the first round retrieval are relevant as feedback documents, and expand the original queries with feedback terms selected from these feedback documents. However, applying PRF for query expansion must be very carefully. Wrongly added terms can bring noisy information and hurt the overall search experiences extensively. The assumption of feedback documents is too strong to be completely true. To avoid noise import and make significant improvements simultaneously, we solve the significant problem through four ways in this dissertation. Firstly, we assume the proximity information among terms as term semantic associations and utilize them to seek new relevant terms. Next, to obtain good and robust performance for PRF via adapting topic information, we propose a new concept named topic space and present three models based on it. Topics obtained through topic modeling do help identify how relevant a feedback document is. Weights of candidate terms in these more relevant feedback documents will be boosted and have higher probabilities to be chosen. Furthermore, we apply machine learning methods to classify which feedback documents are effective for PRF. To solve the problem of lack-of-training-data for the application of machine learning methods in PRF, we improve a traditional co-training method and take the quality of classifiers into account. Finally, we present a new probabilistic framework to integrate existing effective methods like semantic associations as components for further research. All the work has been tested on public datasets and proven to be effective and efficient