Symmetric matrices, Catalan paths, and correlations

Kenyon and Pemantle (2014) gave a formula for the entries of a square matrix in terms of connected principal and almost-principal minors. Each entry is an explicit Laurent polynomial whose terms are the weights of domino tilings of a half Aztec diamond. They conjectured an analogue of this parametrization for symmetric matrices, where the Laurent monomials are indexed by Catalan paths. In this paper we prove the Kenyon-Pemantle conjecture, and apply this to a statistics problem pioneered by Joe (2006). Correlation matrices are represented by an explicit bijection from the cube to the elliptope

A Framework for Systematic Design and Operation of Condition-Based Maintenance Systems: Evidence from a Case Study of Fleet Management at Sea Ports

Ongoing improvement of logistics and intermodal transport leads to high requirements regarding availability of machine resources like straddle carriers or gantry cranes. Accordingly, efficient maintenance strategies for port equipment have to be established. The change to condition-based maintenance strategies promises to save resources while enhancing availability and reliability. This paper introduces a framework of methods and tools that enable the systematic design of condition-based maintenance systems on the one hand and offers integrated support for operating such systems on the other hand. The findings are evaluated based on a case-study of a German seaport and illustrate the usage of the system based on managing the equipping process of machines with sensors for condition monitoring as well as bringing the system into the operation phase