Incremental verification and synthesis of discrete-event systems guided by counter-examples

This article presents new approaches to system verification and synthesis based on subsystem verification and the novel combined use of counterexamples and heuristics to identify suitable subsystems incrementally. The scope of safety properties considered is limited to behavioral inclusion and controllability. The verification examples considered provide a comparison of the approaches presented with straightforward state exploration and an understanding of their applicability in an industrial context

BRST cohomology and Hodge decomposition theorem in Abelian gauge theory

We discuss the Becchi-Rouet-Stora-Tyutin (BRST) cohomology and Hodge decomposition theorem for the two dimensional free U(1) gauge theory. In addition to the usual BRST charge, we derive a local, conserved and nilpotent co(dual)-BRST charge under which the gauge-fixing term remains invariant. We express the Hodge decomposition theorem in terms of these charges and the Laplacian operator. We take a single photon state in the quantum Hilbert space and demonstrate the notion of gauge invariance, no-(anti)ghost theorem, transversality of photon and establish the topological nature of this theory by exploiting the concepts of BRST cohomology and Hodge decomposition theorem. In fact, the topological nature of this theory is encoded in the vanishing of the Laplacian operator when equations of motion are exploited. On the two dimensional compact manifold, we derive two sets of topological invariants with respect to the conserved and nilpotent BRST- and co-BRST charges and express the Lagrangian density of the theory as the sum of terms that are BRST- and co-BRST invariants. Mathematically, this theory captures together some of the key features of both Witten- and Schwarz type of topological field theories.Comment: 20 pages, LaTeX, no figures, Title and text have been changed, Journal reference is given, some references have been adde

A Concise Introduction to Perturbation Theory in Cosmology

We give a concise, self-contained introduction to perturbation theory in cosmology at linear and second order, striking a balance between mathematical rigour and usability. In particular we discuss gauge issues and the active and passive approach to calculating gauge transformations. We also construct gauge-invariant variables, including the second order tensor perturbation on uniform curvature hypersurfaces.Comment: revtex4, 16 pages, 3 figures; v2: minor changes, typos corrected, reference added, version accepted by CQ

Assessing Bottom Gear Impact in the WGOM Closure Area: A Multifaceted Approach

Mashkoor Malik presented the results of a UNH Center for Coastal and Ocean Mapping (CCOM) study of the seafloor of the WGOMCA. Objectives The objectives for the CCOM study were to: • Construct a bathymetric map of Jeffrey’s Ledge to serve as a framework for subsequent studies. • Test the potential use of multibeam sonar to monitor fishing gear impacts. • Determine if it is possible to observe closure impacts with multibeam sonar