Asymptotically exact evolution equations are derived for trains of small amplitude counterpropagating water waves over finite depth. Surface tension is included. The resulting equations are nonlocal and generalize the equations derived by Davey and Stewartson for unidirectional wave trains. The stability properties of stationary standing and quasiperiodic waves are determined as a function of surface tension and fluid depth for both long wavelength longitudinal and transverse perturbations.
This paper reports on methods and results of an applied research project by a team consisting of SAIC and four universities to develop, integrate, and evaluate new approaches to detect the weak signals characteristic of insider threats on organizations' information systems. Our system combines structural and semantic information from a real corporate database of monitored activity on their users' computers to detect independently developed red team inserts of malicious insider activities. We have developed and applied multiple algorithms for anomaly detection based on suspected scenarios of malicious insider behavior, indicators of unusual activities, high-dimensional statistical patterns, temporal sequences, and normal graph evolution. Algorithms and representations for dynamic graph processing provide the ability to scale as needed for enterpriselevel deployments on real-time data streams. We have also developed a visual language for specifying combinations of features, baselines, peer groups, time periods, and algorithms to detect anomalies suggestive of instances of insider threat behavior. We defined over 100 data features in seven categories based on approximately 5.5 million actions per day from approximately 5,500 users. We have achieved area under the ROC curve values of up to 0.979 and lift values of 65 on the top 50 user-days identified on two months of real data.
We rigorously establish the validity of the equations describing the evolution of onedimensional long wavelength modulations of counterpropagating wavetrains for a hyperbolic model equation, namely the sine-Gordon equation. We consider both periodic amplitude functions and localized wavepackets. For the localized case, the wavetrains are completely decoupled at leading order, while in the periodic case the amplitude equations take the form of mean-eld (nonlocal) Schr odinger equations rather than locally coupled partial di erential equations. The origin of this weakened coupling is traced to a hidden translation symmetry in the linear problem, which is related to the existence of a characteristic frame traveling at the group velocity of each wavetrain. It is proved that solutions to the amplitude equations dominate the dynamics of the governing equations on asymptotically long time scales. While the details of the discussion are restricted to the class of model equations having a leading cubic nonlinearity, the results strongly indicate that mean-eld evolution equations are generic for bimodal disturbances in dispersive systems with O(1) group velocity.
The radar backscatter from complex sources, such as ships and ocean waves, can vary rapidly with target aspect or time. The radar cross section (RCS) of such targets is usually described in statistical terms using one of the many statistical models that are available. These models, however, tend to fit less well when the amplitude fluctuations begin to vary over wider extremes and become impulsive in nature. To better handle this condition, the alpha-stable distribution is shown to model RCS over a wide range of amplitudes. The alpha-stable distribution is derived from the generalized central limit theorem and contains the Gaussian (or Rayleigh) distribution as a subset. The alpha-stable distribution is shown to fit examples of S h p RCS as well as sea clutter examples. The performance of various envelope detectors including the maximum likelihood detector for the alpha-stable distribution is shown for a low signal-to-noise (SNR) case. 1 .O INTRODUCTION The envelope of the backscatter from complex radar targets can vary rapidly with changing aspect angle (Nathanson, 1969). Because of the amplitude fluctuations, the RCS is best characterized using statistical terms such as averages, medians and distributions. Commonly used distribution functions (single pulse; envelope or envelope squared) for target modeling analysis include: Rayleigh (Swerling cases 1 and 2), chi-square (Swerling cases 3 and 4 for four degrees-of-freedom), Rician, log-normal, and Weibull. The finite RCS, beta distribution (Maffett, 1989) has also been advocated. The density functions and their parameters form RCS distribution models or statistical RCS models. Because of large mean-to-median ratios, the RCS distribution of ships, for example, have been represented by the log-normal distribution (Nathanson, 1969). The models are used to predict target detectability. Next, when modeling the radar backscatter from ocean waves, sea clutter returns change rapidly with time. The radar returns are generally more spiky for horizontally polarized measurements and for high spatial resolution measurements. The K-distribution is currently a widely accepted model for representing the amplitude or envelope statistics of sea clutter (Armstrong, 1991 and, Nohara 1991). This distribution is based on the assumption that the radar return from a region consists of the sum of independent returns (speckle with "short" decorrelation time) that vary in intensity (chi-distributed) with time (modulation with "long" decorrelation time). Knowledge of the distribution can result in detector designs that are tailored to the clutter statistics. Applying conventional distributions to targets or sea clutter can become less accurate when the returns are more impulsive or spiky in nature (large mean-to-median ratio). Estimates of statistics such as the mean RCS (arithmetic average of the envelope squared, or mean-square of the envelope) can give inconsistent results. To avoid giving too much weight to the large spikes, the conventional approaches are to ignore the spikes (treat as...
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