Rigorous Results for Hierarchical Models of Structural Glasses

Intersecting loop models on Z: rigorous results

Ž . We consider a general class of intersecting loop models in d dimensions, including those related to high-temperature expansions of well-known spin models. We find that the loop models exhibit some interesting features – often in the ‘‘unphysical’’ region of parameter space where all connection with the original spin Hamiltonian is apparently lost. For a particular ns2, ds2 model, we establi...

Rigorous results for a hierarchy of generalized Heisenberg models.

The Lieb-Schultz-Mattis theorem is extended to generalized Heisenberg models related to unexceptional Lie algebras. It is shown that there are no energy gaps above the ground states for SO(4), Sp(2), and SU(4) Heisenberg models; but gaps are suspected to occur in SO(5) and SO(6) models. The nondegenerate ground state for these models is rigorously proven.

Structural EM for Hierarchical Latent Class Models

Hierarchical latent class (HLC) models are tree-structured Bayesian networks where leaf nodes are observed while internal nodes are not. This paper is concerned with the problem of learning HLC models from data. We apply the idea of structural EM to a hill-climbing algorithm for this task described in an accompanying paper (Zhang et al. 2003) and show empirically that the improved algorithm can...

Fuzzy Hierarchical Location-Allocation Models for Congested Systems

There exist various service systems that have hierarchical structure. In hierarchical service networks, facilities at different levels provide different types of services. For example, in health care systems, general centers provide low-level services such as primary health care services, while the specialized hospitals provide high-level services. Because of demand congestion in service networ...

Institute for Mathematical Physics Quantum Dots a Survey of Rigorous Results a Survey of Rigorous Results