Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions

We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an exactly solvable high-spin asymmetric quantum Hamiltonian that is the infinitesimal generator of the zero range process. Generally, the critical dynamics of the interface fluctuations is in the Kardar-Parisi-Zhang universality class of critical behavior. We remark that a whole family of RSOS interface models similar to the Ising interface model investigated here can be described by exactly solvable restricted high-spin quantum XXZ-type Hamiltonians. (C) 2012 Elsevier B.V. All rights reserved.

Network-based stochastic semisupervised learning

Semisupervised learning is a machine learning approach that is able to employ both labeled and unlabeled samples in the training process. In this paper, we propose a semisupervised data classification model based on a combined random-preferential walk of particles in a network (graph) constructed from the input dataset. The particles of the same class cooperate among themselves, while the particles of different classes compete with each other to propagate class labels to the whole network. A rigorous model definition is provided via a nonlinear stochastic dynamical system and a mathematical analysis of its behavior is carried out. A numerical validation presented in this paper confirms the theoretical predictions. An interesting feature brought by the competitive-cooperative mechanism is that the proposed model can achieve good classification rates while exhibiting low computational complexity order in comparison to other network-based semisupervised algorithms. Computer simulations conducted on synthetic and real-world datasets reveal the effectiveness of the model.