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Moment invariants [functions of the moments of a Vlasov distribution that are invariant under Sp(6)] are classified using Young diagrams. The connection between the moment invariants and the Poincaré invariants is established. An application using the moment invariants as phase space coordinates is considered for a matching section in a particle-beam accelerator, and a Lie–Poisson numerical integration algorithm for the moment dynamics is proposed.

This report describes work done during FY 95 that was sponsored by the Department of Energy, Office of Nonproliferation and National Security, Knowledge Fusion Project. The project team selected satellite sensor data to use as the one main example for the application of its analysis algorithms. The specific sensorfusion problem has many generic features, which make it a worthwhile problem to attempt to solve in a general way. The generic problem is to recognize events of interest from multiple time series that define a possibly noisy background. By implementing a suite of time series modeling and forecasting methods and using well-chosen alarm criteria, we reduce the number of false alarms. We then further reduce the number of false alarms by analyzing all suspicious sections of data, as judged by the alarm criteria, with pattern recognition methods. An accompanying report (Ref. 1) describes the implementation and application of this 2-step process for separating events from unusual background and applies a suite of forecasting methods followed by a suite of pattern recognition methods. This report goes into more detail about one of the forecasting methods and one of the pattern recognition methods and is applied to the same kind of satellite-sensor data that is described in Ref.1.