Gravity and Discrete Symmetry

Using the differential calculus on discrete group, we study the general relativity in the space-time which is the product of a four dimensional manifold by a two-point space. We generalize the usual concept of frame and connection in our space-time, and from the generalized torsion free condition we obtain an action of a scalar field coupled to Einstein gravity, which may be related to the Jordan-Brans-Dicke theory.Comment: 1

iTrace: An Implicit Trust Inference Method for Trust-aware Collaborative Filtering

The growth of Internet commerce has stimulated the use of collaborative filtering (CF) algorithms as recommender systems. A collaborative filtering (CF) algorithm recommends items of interest to the target user by leveraging the votes given by other similar users. In a standard CF framework, it is assumed that the credibility of every voting user is exactly the same with respect to the target user. This assumption is not satisfied and thus may lead to misleading recommendations in many practical applications. A natural countermeasure is to design a trust-aware CF (TaCF) algorithm, which can take account of the difference in the credibilities of the voting users when performing CF. To this end, this paper presents a trust inference approach, which can predict the implicit trust of the target user on every voting user from a sparse explicit trust matrix. Then an improved CF algorithm termed iTrace is proposed, which takes advantage of both the explicit and the predicted implicit trust to provide recommendations with the CF framework. An empirical evaluation on a public dataset demonstrates that the proposed algorithm provides a significant improvement in recommendation quality in terms of mean absolute error (MAE).Comment: 6 pages, 4 figures, 1 tabl