Self-Consistent Analysis of OH-Zeeman Observations: Too Much Noise about Noise

We had recently re-analyzed in a self-consistent way OH-Zeeman observations in four molecular-cloud envelopes and we had shown that, contrary to claims by Crutcher et al., there is no evidence that the mass-to-flux ratio decreases from the envelopes to the cores of these clouds. The key difference between our data analysis and the earlier one by Crutcher et al. is the relaxation of the overly restrictive assumption made by Crutcher et al, that the magnetic field strength is independent of position in each of the four envelopes. In a more recent paper, Crutcher et al. (1) claim that our analysis is not self-consistent, in that it misses a cosine factor, and (2) present new arguments to support their contention that the magnetic-field strength is indeed independent of position in each of the four envelopes. We show that the claim of the missing cosine factor is false, that the new arguments contain even more serious problems than the Crutcher et al. original data analysis, and we present new observational evidence, independent of the OH-Zeeman data, that suggests significant variations in the magnetic-field strength in the four cloud envelopes.Comment: 8 pages, 3 figures, MNRAS in pres

Complex Structure in Class 0 Protostellar Envelopes II: Kinematic Structure from Single-Dish and Interferometric Molecular Line Mapping

We present a study of dense molecular gas kinematics in seventeen nearby protostellar systems using single-dish and interferometric molecular line observations. The non-axisymmetric envelopes around a sample of Class 0/I protostars were mapped in the N2H+ (J=1-0) tracer with the IRAM 30m, CARMA and PdBI as well as NH3 (1,1) with the VLA. The molecular line emission is used to construct line-center velocity and linewidth maps for all sources to examine the kinematic structure in the envelopes on spatial scales from 0.1 pc to ~1000 AU. The direction of the large-scale velocity gradients from single-dish mapping is within 45 degrees of normal to the outflow axis in more than half the sample. Furthermore, the velocity gradients are often quite substantial, the average being ~2.3 km\s\pc. The interferometric data often reveal small-scale velocity structure, departing from the more gradual large-scale velocity gradients. In some cases, this likely indicates accelerating infall and/or rotational spin-up in the inner envelope; the median velocity gradient from the interferometric data is ~10.7 km/s/pc. In two systems, we detect high-velocity HCO+ (J=1-0) emission inside the highest-velocity \nthp\ emission. This enables us to study the infall and rotation close to the disk and estimate the central object masses. The velocity fields observed on large and small-scales are more complex than would be expected from rotation alone, suggesting that complex envelope structure enables other dynamical processes (i.e. infall) to affect the velocity field.Comment: 85 Pages, 31 Figures, 11 Tables, Accepted to ApJ

The spectral analysis of nonstationary categorical time series using local spectral envelope

Most classical methods for the spectral analysis are based on the assumption that the time series is stationary. However, many time series in practical problems shows nonstationary behaviors. The data from some fields are huge and have variance and spectrum which changes over time. Sometimes,we are interested in the cyclic behavior of the categorical-valued time series such as EEG sleep state data or DNA sequence, the general method is to scale the data, that is, assign numerical values to the categories and then use the periodogram to find the cyclic behavior. But there exists numerous possible scaling. If we arbitrarily assign the numerical values to the categories and proceed with a spectral analysis, then the results will depend on the particular assignment. We would like to find the all possible scaling that bring out all of the interesting features in the data. To overcome these problems, there have been many approaches in the spectral analysis. Our goal is to develop a statistical methodology for analyzing nonstationary categorical time series in the frequency domain. In this dissertation, the spectral envelope methodology is introduced for spectral analysis of categorical time series. This provides the general framework for the spectral analysis of the categorical time series and summarizes information from the spectrum matrix. To apply this method to nonstationary process, I used the TBAS(Tree-Based Adaptive Segmentation) and local spectral envelope based on the piecewise stationary process. In this dissertation,the TBAS(Tree-Based Adpative Segmentation) using distance function based on the Kullback-Leibler divergence was proposed to find the best segmentation

Adjustment of interaural-time-difference analysis to sound level

To localize low-frequency sound sources in azimuth, the binaural system compares the timing of sound waves at the two ears with microsecond precision. A similarly high precision is also seen in the binaural processing of the envelopes of high-frequency complex sounds. Both for low- and high-frequency sounds, interaural time difference (ITD) acuity is to a large extent independent of sound level. The mechanisms underlying this level-invariant extraction of ITDs by the binaural system are, however, only poorly understood. We use high-frequency pip trains with asymmetric and dichotic pip envelopes in a combined psychophysical, electrophysiological, and modeling approach. Although the dichotic envelopes cannot be physically matched in terms of ITD, the match produced perceptually by humans is very reliable, and it depends systematically on the overall sound level. These data are reflected in neural responses from the gerbil lateral superior olive and lateral lemniscus. The results are predicted in an existing temporal-integration model extended with a level-dependent threshold criterion. These data provide a very sensitive quantification of how the peripheral temporal code is conditioned for binaural analysis

Asymptotic power of sphericity tests for high-dimensional data

This paper studies the asymptotic power of tests of sphericity against perturbations in a single unknown direction as both the dimensionality of the data and the number of observations go to infinity. We establish the convergence, under the null hypothesis and contiguous alternatives, of the log ratio of the joint densities of the sample covariance eigenvalues to a Gaussian process indexed by the norm of the perturbation. When the perturbation norm is larger than the phase transition threshold studied in Baik, Ben Arous and Peche [Ann. Probab. 33 (2005) 1643-1697] the limiting process is degenerate, and discrimination between the null and the alternative is asymptotically certain. When the norm is below the threshold, the limiting process is nondegenerate, and the joint eigenvalue densities under the null and alternative hypotheses are mutually contiguous. Using the asymptotic theory of statistical experiments, we obtain asymptotic power envelopes and derive the asymptotic power for various sphericity tests in the contiguity region. In particular, we show that the asymptotic power of the Tracy-Widom-type tests is trivial (i.e., equals the asymptotic size), whereas that of the eigenvalue-based likelihood ratio test is strictly larger than the size, and close to the power envelope.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1100 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Beyond bathymetry: Mapping acoustic backscattering from the deep seafloor with Sea Beam

In its standard mode of operation, the multibeam echosounder Sea Beam produces high resolution bathymetric contour charts of the seafloor surveyed. However, additional information about the nature of the seafloor can be extracted from the structure of the echo signals received by the system. Such signals have been recorded digitally over a variety of seafloor environments for which independent observations from bottom photographs or sidescan sonars were available. An attempt is made to relate the statistical properties of the bottom‐backscattered sound field to the independently observed geologicalcharacteristics of the seafloor surveyed. Acoustic boundary mapping over flat areas is achieved by following trend changes in the acoustic data both along and across track. Such changes in the acoustics are found to correlate with changes in bottom type or roughness structure. The overall energy level of a partial angular‐dependence function of backscattering appears to depend strongly on bottom type, whereas the shape of the function does not. Clues to the roughness structure of the bottom are obtained by relating the shape of the probability density function of normal‐incidence echo envelopes to the degree of coherence in the backscattered acoustic field