48,010 research outputs found
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
Theta operators, Goss polynomials, and v-adic modular forms
We investigate hyperderivatives of Drinfeld modular forms and determine
formulas for these derivatives in terms of Goss polynomials for the kernel of
the Carlitz exponential. As a consequence we prove that v-adic modular forms in
the sense of Serre, as defined by Goss and Vincent, are preserved under
hyperdifferentiation. Moreover, upon multiplication by a Carlitz factorial,
hyperdifferentiation preserves v-integrality.Comment: 20 page
Deriving N-soliton solutions via constrained flows
The soliton equations can be factorized by two commuting x- and t-constrained
flows. We propose a method to derive N-soliton solutions of soliton equations
directly from the x- and t-constrained flows.Comment: 8 pages, AmsTex, no figures, to be published in Journal of Physics
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