Effects of uncertainty on manual tracking performance

Transient phenomena and target acquisition modes associated with interrupted observations during ground-to-air AA tracking were investigated. Using a two-axes control stick, the subjects tracked a computer-generated airplane image on a CRT display. The airplane image excuted a low-level straight pass. At certain pseudo-random times during each 25-second run, the screen was blanked for a period of one second. When the target image reappeared, the subjects reacquired it and continued tracking, attempting to minimize vector RMS error for the entire run (including the blanked period). The results reveal an increase both in tracking error and in error variance during the blanked period, only when the target disappears while in the crossover region. Blanking at other times effected increased variance but had no effect on the mean error. A blanking period just before crossover produced an increase lag while a blanking just after crossover resulted in a lead and thus made the error curve more symmetric

Polarized Scattering in the Vicinty of Galaxies

Some bright cD galaxies in cluster cooling flows have Thomson optical depths exceeding 0.01. A few percent of their luminosity is scattered and appears as diffuse polarized emission. We calculate the scattering process for different geometric combinations of luminosity sources and scattering media. We apply our results to galaxies, with and without active nuclei, immersed in cooling flows. We model observations of NGC 1275 and M87 (without active nuclei) in the presence of sky and galactic background fluxes which hinder the measurement of the scattered light at optical wavelengths. Current instruments are unable to detect the scattered light from such objects. However, when a galaxy has an active nucleus of roughly the same luminosity as the remainder of the galaxy in V, both the total and polarized scattered intensity should observable on large scales (5--30kpc), meaning intensity levels greater than 1% of the background level. For typical AGN and galaxy spectral distributions, the scattering is most easily detected at short (U) wavelengths. We point out that a number of such cases will occur. We show that the radiation pattern from the central nuclear region can be mapped using the scattering. We also show that the scattered light can be used to measure inhomogeneities in the cooling flow.Comment: 29 pages of TEX, 14 figs, CRSR-1046, in ApJ Nov 20, 199

Optimal sequential fingerprinting: Wald vs. Tardos

We study sequential collusion-resistant fingerprinting, where the fingerprinting code is generated in advance but accusations may be made between rounds, and show that in this setting both the dynamic Tardos scheme and schemes building upon Wald's sequential probability ratio test (SPRT) are asymptotically optimal. We further compare these two approaches to sequential fingerprinting, highlighting differences between the two schemes. Based on these differences, we argue that Wald's scheme should in general be preferred over the dynamic Tardos scheme, even though both schemes have their merits. As a side result, we derive an optimal sequential group testing method for the classical model, which can easily be generalized to different group testing models.Comment: 12 pages, 10 figure

Lectures on Linear Stability of Rotating Black Holes

These lecture notes are concerned with linear stability of the non-extreme Kerr geometry under perturbations of general spin. After a brief review of the Kerr black hole and its symmetries, we describe these symmetries by Killing fields and work out the connection to conservation laws. The Penrose process and superradiance effects are discussed. Decay results on the long-time behavior of Dirac waves are outlined. It is explained schematically how the Maxwell equations and the equations for linearized gravitational waves can be decoupled to obtain the Teukolsky equation. It is shown how the Teukolsky equation can be fully separated to a system of coupled ordinary differential equations. Linear stability of the non-extreme Kerr black hole is stated as a pointwise decay result for solutions of the Cauchy problem for the Teukolsky equation. The stability proof is outlined, with an emphasis on the underlying ideas and methods.Comment: 25 pages, LaTeX, 3 figures, lectures given at first DOMOSCHOOL in July 2018, minor improvements (published version

The Cosmological Constant and Advanced Gravitational Wave Detectors

Interferometric gravitational wave detectors could measure the frequency sweep of a binary inspiral [characterized by its chirp mass] to high accuracy. The observed chirp mass is the intrinsic chirp mass of the binary source multiplied by $(1+z)$, where $z$ is the redshift of the source. Assuming a non-zero cosmological constant, we compute the expected redshift distribution of observed events for an advanced LIGO detector. We find that the redshift distribution has a robust and sizable dependence on the cosmological constant; the data from advanced LIGO detectors could provide an independent measurement of the cosmological constant.Comment: 13 pages plus 5 figure, LaTeX. Revised and final version, to appear in Phys. Rev.

QUANTIZATION OF A CLASS OF PIECEWISE AFFINE TRANSFORMATIONS ON THE TORUS

We present a unified framework for the quantization of a family of discrete dynamical systems of varying degrees of "chaoticity". The systems to be quantized are piecewise affine maps on the two-torus, viewed as phase space, and include the automorphisms, translations and skew translations. We then treat some discontinuous transformations such as the Baker map and the sawtooth-like maps. Our approach extends some ideas from geometric quantization and it is both conceptually and calculationally simple.Comment: no. 28 pages in AMSTE

Pseudospectral Calculation of the Wavefunction of Helium and the Negative Hydrogen Ion

We study the numerical solution of the non-relativistic Schr\"{o}dinger equation for two-electron atoms in ground and excited S-states using pseudospectral (PS) methods of calculation. The calculation achieves convergence rates for the energy, Cauchy error in the wavefunction, and variance in local energy that are exponentially fast for all practical purposes. The method requires three separate subdomains to handle the wavefunction's cusp-like behavior near the two-particle coalescences. The use of three subdomains is essential to maintaining exponential convergence. A comparison of several different treatments of the cusps and the semi-infinite domain suggest that the simplest prescription is sufficient. For many purposes it proves unnecessary to handle the logarithmic behavior near the three-particle coalescence in a special way. The PS method has many virtues: no explicit assumptions need be made about the asymptotic behavior of the wavefunction near cusps or at large distances, the local energy is exactly equal to the calculated global energy at all collocation points, local errors go down everywhere with increasing resolution, the effective basis using Chebyshev polynomials is complete and simple, and the method is easily extensible to other bound states. This study serves as a proof-of-principle of the method for more general two- and possibly three-electron applications.Comment: 23 pages, 20 figures, 2 tables, Final refereed version - Some references added, some stylistic changes, added paragraph to matrix methods section, added last sentence to abstract

Evidence for an oscillatory singularity in generic U(1) symmetric cosmologies on T3×RT^3 \times R

A longstanding conjecture by Belinskii, Lifshitz, and Khalatnikov that the singularity in generic gravitational collapse is locally oscillatory is tested numerically in vacuum, U(1) symmetric cosmological spacetimes on $T^3 \times R$. If the velocity term dominated (VTD) solution to Einstein's equations is substituted into the Hamiltonian for the full Einstein evolution equations, one term is found to grow exponentially. This generates a prediction that oscillatory behavior involving this term and another (which the VTD solution causes to decay exponentially) should be observed in the approach to the singularity. Numerical simulations strongly support this prediction.Comment: 15 pages, Revtex, includes 12 figures, psfig. High resolution versions of figures 7, 8, 9, and 11 may be obtained from anonymous ftp to ftp://vela.acs.oakland.edu/pub/berger/u1genfig

Mining Uncertain Sequential Patterns in Iterative MapReduce

This paper proposes a sequential pattern mining (SPM) algorithm in large scale uncertain databases. Uncertain sequence databases are widely used to model inaccurate or imprecise timestamped data in many real applications, where traditional SPM algorithms are inapplicable because of data uncertainty and scalability. In this paper, we develop an efficient approach to manage data uncertainty in SPM and design an iterative MapReduce framework to execute the uncertain SPM algorithm in parallel. We conduct extensive experiments in both synthetic and real uncertain datasets. And the experimental results prove that our algorithm is efficient and scalable