41,193 research outputs found
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
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