Deconvolution of point processes

The superposition of two independent point processes can be described by multiplication of their probability generating functionals (p.g.fl.s). The inverse operation, which can be viewed as a deconvolution, is defined by dividing the superposed process by one of its constituent p.g.fl.s. The deconvolved process is computed using the higher-order chain rule for Gateaux differentials. The higher-order quotient rule for Gateaux differentials is first established and then applied to point processes

Faà di Bruno’s formula and spatial cluster modelling

AbstractThe probability generating functional (p.g.fl.) provides a useful means of compactly representing point process models. Cluster processes can be described through the composition of p.g.fl.s, and factorial moment measures and Janossy measures can be recovered from the p.g.fl. using variational derivatives. This article describes the application of a recent result in variational calculus, a generalisation of Faà di Bruno’s formula, to determine such results for cluster processes

Regional variance for multi-object filtering

Recent progress in multi-object filtering has led to algorithms that compute the first-order moment of multi-object distributions based on sensor measurements. The number of targets in arbitrarily selected regions can be estimated using the first-order moment. In this work, we introduce explicit formulae for the computation of the second-order statistic on the target number. The proposed concept of regional variance quantifies the level of confidence on target number estimates in arbitrary regions and facilitates information-based decisions. We provide algorithms for its computation for the Probability Hypothesis Density (PHD) and the Cardinalized Probability Hypothesis Density (CPHD) filters. We demonstrate the behaviour of the regional statistics through simulation examples

Analysis of routine communication in the air traffic control system

The present project has three related goals. The first is to describe the organization of routine controller-pilot communication. This includes identifying the basic units of communication and how they are organized into discourse, how controllers and pilots use language to achieve their goals, and what topics they discuss. The second goal is to identify the type and frequency of problems that interrupt routine information transfer and prompt pilots and controllers to focus on the communication itself. The authors analyze the costs of these problems in terms of communication efficiency, and the techniques used to resolve these problems. Third, the authors hope to identify factors associated with communication problems, such as deviations from conventional air traffic control procedures

Metal-Insulator Transition Revisited for Cold Atoms in Non-Abelian Gauge Potentials

We discuss the possibility of realizing metal-insulator transitions with ultracold atoms in two-dimensional optical lattices in the presence of artificial gauge potentials. Such transitions have been extensively studied for magnetic fields corresponding to Abelian gauges; they occur when the magnetic flux penetrating the lattice plaquette is an irrational multiple of the magnetic flux quantum. Here we present the first study of these transitions for non-Abelian U(2) gauge fields, which can be realized with atoms with two pairs of degenerate internal states. In contrast to the Abelian case, the spectrum and localization transition in the non-Abelian case is strongly influenced by atomic momenta. In addition to determining the localization boundary, the momentum fragments the spectrum and the minimum energy viewed as a function of momentum exhibits a step structure. Other key characteristics of the non-Abelian case include the absence of localization for certain states and satellite fringes around the Bragg peaks in the momentum distribution and an interesting possibility that the transition can be tuned by the atomic momenta.Comment: 4 pages, 4 figures, see http://physics.gmu.edu/~isatija/recentpub.htm for high resolution figure