Integrable dispersionless KdV hierarchy with sources

An integrable dispersionless KdV hierarchy with sources (dKdVHWS) is derived. Lax pair equations and bi-Hamiltonian formulation for dKdVHWS are formulated. Hodograph solution for the dispersionless KdV equation with sources (dKdVWS) is obtained via hodograph transformation. Furthermore, the dispersionless Gelfand-Dickey hierarchy with sources (dGDHWS) is presented.Comment: 15 pages, to be published in J. Phys. A: Math. Ge

Improving information filtering via network manipulation

Recommender system is a very promising way to address the problem of overabundant information for online users. Though the information filtering for the online commercial systems received much attention recently, almost all of the previous works are dedicated to design new algorithms and consider the user-item bipartite networks as given and constant information. However, many problems for recommender systems such as the cold-start problem (i.e. low recommendation accuracy for the small degree items) are actually due to the limitation of the underlying user-item bipartite networks. In this letter, we propose a strategy to enhance the performance of the already existing recommendation algorithms by directly manipulating the user-item bipartite networks, namely adding some virtual connections to the networks. Numerical analyses on two benchmark data sets, MovieLens and Netflix, show that our method can remarkably improve the recommendation performance. Specifically, it not only improve the recommendations accuracy (especially for the small degree items), but also help the recommender systems generate more diverse and novel recommendations.Comment: 6 pages, 5 figure