XOR-Sampling for Network Design with Correlated Stochastic Events

Many network optimization problems can be formulated as stochastic network design problems in which edges are present or absent stochastically. Furthermore, protective actions can guarantee that edges will remain present. We consider the problem of finding the optimal protection strategy under a budget limit in order to maximize some connectivity measurements of the network. Previous approaches rely on the assumption that edges are independent. In this paper, we consider a more realistic setting where multiple edges are not independent due to natural disasters or regional events that make the states of multiple edges stochastically correlated. We use Markov Random Fields to model the correlation and define a new stochastic network design framework. We provide a novel algorithm based on Sample Average Approximation (SAA) coupled with a Gibbs or XOR sampler. The experimental results on real road network data show that the policies produced by SAA with the XOR sampler have higher quality and lower variance compared to SAA with Gibbs sampler.Comment: In Proceedings of the Twenty-sixth International Joint Conference on Artificial Intelligence (IJCAI-17). The first two authors contribute equall

Dynamical Condensation in a Holographic Superconductor Model with Anisotropy

We study dynamical condensation process in a holographic superconductor model with anisotropy. The time-dependent numerical solution is constructed for the Einstein-Maxwell-dilaton theory with complex scalar in asymptotic AdS spacetime. The introduction of dilaton field generates the anisotropy in boundary spatial directions. In analogy of isotropic case, we have two black hole solutions below certain critical temperature $T_c$, the anisotropic charged black hole with and without scalar hair, corresponding respectively to the supercooled normal phase and superconducting phase in the boundary theory. We observe a nonlinear evolution from a supercooled anisotropic black hole without scalar hair to a anisotropic hairy black hole. Via AdS/CFT correspondence, we extract time evolution of the condensate operator, which shows an exponential growth and subsequent saturation, similar to the isotropic case. Furthermore, we obtain a nontrivial time evolution of the boundary pressure, while in isotropic case it remains a constant. We also generalize quasinormal modes calculation to anisotropic black holes and shows scalar quasinormal modes match with relaxation time scale of the condensate operator. In addition, we present the final temperature and anisotropic pressure as functions of initial temperature and background anisotropy.Comment: 18 pages, 12 figures. v2: minor revision and references adde