7,117 research outputs found
On the denominators of harmonic numbers
Let be the -th harmonic number and let be its denominator. It
is well known that is even for every integer . In this paper, we
study the properties of . One of our results is: the set of positive
integers such that is divisible by the least common multiple of has density one. In particular, for any
positive integer , the set of positive integers such that is
divisible by has density one.Comment: 6 page
Recommender Systems with Characterized Social Regularization
Social recommendation, which utilizes social relations to enhance recommender
systems, has been gaining increasing attention recently with the rapid
development of online social network. Existing social recommendation methods
are based on the fact that users preference or decision is influenced by their
social friends' behaviors. However, they assume that the influences of social
relation are always the same, which violates the fact that users are likely to
share preference on diverse products with different friends. In this paper, we
present a novel CSR (short for Characterized Social Regularization) model by
designing a universal regularization term for modeling variable social
influence. Our proposed model can be applied to both explicit and implicit
iteration. Extensive experiments on a real-world dataset demonstrate that CSR
significantly outperforms state-of-the-art social recommendation methods.Comment: to appear in CIKM 201
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