Classical O(N) nonlinear sigma model on the half line: a study on consistent Hamiltonian description

The problem of consistent Hamiltonian structure for O(N) nonlinear sigma model in the presence of five different types of boundary conditions is considered in detail. For the case of Neumann, Dirichlet and the mixture of these two types of boundaries, the consistent Poisson brackets are constructed explicitly, which may be used, e.g. for the construction of current algebras in the presence of boundary. While for the mixed boundary conditions and the mixture of mixed and Dirichlet boundary conditions, we prove that there is no consistent Poisson brackets, showing that the mixed boundary conditions are incompatible with all nontrivial subgroups of $O((N)$.Comment: revtex4, 7pp, bibte

Leveraging Node Attributes for Incomplete Relational Data

Relational data are usually highly incomplete in practice, which inspires us to leverage side information to improve the performance of community detection and link prediction. This paper presents a Bayesian probabilistic approach that incorporates various kinds of node attributes encoded in binary form in relational models with Poisson likelihood. Our method works flexibly with both directed and undirected relational networks. The inference can be done by efficient Gibbs sampling which leverages sparsity of both networks and node attributes. Extensive experiments show that our models achieve the state-of-the-art link prediction results, especially with highly incomplete relational data.Comment: Appearing in ICML 201