Multi-scale window specification over streaming trajectories

Enormous amounts of positional information are collected by monitoring applications in domains such as fleet management cargo transport wildlife protection etc. With the advent of modern location-based services processing such data mostly focuses on providing real-time response to a variety of user requests in continuous and scalable fashion. An important class of such queries concerns evolving trajectories that continuously trace the streaming locations of moving objects like GPS-equipped vehicles commodities with RFID\u27s people with smartphones etc. In this work we propose an advanced windowing operator that enables online incremental examination of recent motion paths at multiple resolutions for numerous point entities. When applied against incoming positions this window can abstract trajectories at coarser representations towards the past while retaining progressively finer features closer to the present. We explain the semantics of such multi-scale sliding windows through parameterized functions that reflect the sequential nature of trajectories and can effectively capture their spatiotemporal properties. Such window specification goes beyond its usual role for non-blocking processing of multiple concurrent queries. Actually it can offer concrete subsequences from each trajectory thus preserving continuity in time and contiguity in space along the respective segments. Further we suggest language extensions in order to express characteristic spatiotemporal queries using windows. Finally we discuss algorithms for nested maintenance of multi-scale windows and evaluate their efficiency against streaming positional data offering empirical evidence of their benefits to online trajectory processing

Symmetries, Stability, and Control in Nonlinear Systems and Networks

This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence analysis tools based on nonlinear contraction theory and virtual dynamical systems. This synergy between structural properties (symmetries) and convergence properties (contraction) is illustrated in the contexts of network motifs arising e.g. in genetic networks, of invariance to environmental symmetries, and of imposing different patterns of synchrony in a network.Comment: 16 pages, second versio

Astrometric and Timing Effects of Gravitational Waves from Localized Sources

A consistent approach for an exhaustive solution of the problem of propagation of light rays in the field of gravitational waves emitted by a localized source of gravitational radiation is developed in the first post-Minkowskian and quadrupole approximation of General Relativity. We demonstrate that the equations of light propagation in the retarded gravitational field of an arbitrary localized source emitting quadrupolar gravitational waves can be integrated exactly. The influence of the gravitational field on the light propagation is examined not only in the wave zone but also in cases when light passes through the intermediate and near zones of the source. Explicit analytic expressions for light deflection and integrated time delay (Shapiro effect) are obtained accounting for all possible retardation effects and arbitrary relative locations of the source of gravitational waves, that of light rays, and the observer. It is shown that the ADM and harmonic gauge conditions can both be satisfied simultaneously outside the source of gravitational waves. Their use drastically simplifies the integration of light propagation equations and those for the motion of light source and observer in the field of the source of gravitational waves, leading to the unique interpretation of observable effects. The two limiting cases of small and large values of impact parameter are elaborated in more detail. Explicit expressions for Shapiro effect and deflection angle are obtained in terms of the transverse-traceless part of the space-space components of the metric tensor. We also discuss the relevance of the developed formalism for interpretation of radio interferometric and timing observations, as well as for data processing algorithms for future gravitational wave detectors.Comment: 43 pages, 4 Postscript figures, uses revtex.sty, accepted to Phys. Rev. D, minor corrections in formulae regarding algebraic sign

A Review of Modeling and Diagnostic Techniques for Eccentricity Fault in Electric Machines

Research on the modeling and fault diagnosis of rotor eccentricities has been conducted during the past two decades. A variety of diagnostic theories and methods have been proposed based on different mechanisms, and there are reviews following either one type of electric machines or one type of eccentricity. Nonetheless, the research routes of modeling and diagnosis are common, regardless of machine or eccentricity types. This article tends to review all the possible modeling and diagnostic approaches for all common types of electric machines with eccentricities and provide suggestions on future research roadmap. The paper indicates that a reliable low-cost non-intrusive real-time online visualized diagnostic method is the trend. Observer-based diagnostic strategies are thought promising for the continued research

Estimation of geopotential from satellite-to-satellite range rate data: Numerical results

A technique for high-resolution geopotential field estimation by recovering the harmonic coefficients from satellite-to-satellite range rate data is presented and tested against both a controlled analytical simulation of a one-day satellite mission (maximum degree and order 8) and then against a Cowell method simulation of a 32-day mission (maximum degree and order 180). Innovations include: (1) a new frequency-domain observation equation based on kinetic energy perturbations which avoids much of the complication of the usual Keplerian element perturbation approaches; (2) a new method for computing the normalized inclination functions which unlike previous methods is both efficient and numerically stable even for large harmonic degrees and orders; (3) the application of a mass storage FFT to the entire mission range rate history; (4) the exploitation of newly discovered symmetries in the block diagonal observation matrix which reduce each block to the product of (a) a real diagonal matrix factor, (b) a real trapezoidal factor with half the number of rows as before, and (c) a complex diagonal factor; (5) a block-by-block least-squares solution of the observation equation by means of a custom-designed Givens orthogonal rotation method which is both numerically stable and tailored to the trapezoidal matrix structure for fast execution