We aim here at obtaining bounds on the first non-null eigenvalue for self-adjoint boundary value problems on a weighted network by means of equilibrium measures, that includes the study of Dirichlet, Neumann and Mixed problems. We also show the sharpness of these bounds throughout the analysis of some known examples. In particular, we emphasize the case of distance-regular graphs, and we show t...

Simulation distances are essentially an approximation of simulation which provide a measure of the extent by which behaviors in systems are inequivalent. In this paper, we consider the general quantitative model of weighted transition systems, where transitions are labeled with elements of a finite metric space. We study the so-called point-wise and accumulating simulation distances which provi...

We consider a generalization of the point-to-point (and single-source) shortest path problem to instances where the shortest path must satisfy a formal language constraint. Given an alphabet Σ, a (directed) network G whose edges are weighted and Σ-labeled, and a regular grammar L ⊆ Σ, the Regular Language Constrained Shortest Path problem consists of finding a shortest path p in G complying wit...