A Generalization of Levy\u27s Concentration-Variance Inequality

Sharp lower bounds are found for the concentration of a probability distribution as a function of the expectation of any given convex symmetric function φ. In the case φ(x)=(x-c)2, where c is the expected value of the distribution, these bounds yield the classical concentration-variance inequality of Lévy. An analogous sharp inequality is obtained in a similar linear search setting, where a sharp lower bound for the concentration is found as a function of the maximum probability swept out from a fixed starting point by a path of given length

Ultraviolet Diversity of Type Ia Supernovae

Ultraviolet (UV) observations of Type Ia supernovae (SNe Ia) probe the outermost layers of the explosion, and UV spectra of SNe Ia are expected to be extremely sensitive to differences in progenitor composition and the details of the explosion. Here we present the first study of a sample of high signal-to-noise ratio SN Ia spectra that extend blueward of 2900 A. We focus on spectra taken within 5 days of maximum brightness. Our sample of ten SNe Ia spans the majority of the parameter space of SN Ia optical diversity. We find that SNe Ia have significantly more diversity in the UV than in the optical, with the spectral variance continuing to increase with decreasing wavelengths until at least 1800 A (the limit of our data). The majority of the UV variance correlates with optical light-curve shape, while there are no obvious and unique correlations between spectral shape and either ejecta velocity or host-galaxy morphology. Using light-curve shape as the primary variable, we create a UV spectral model for SNe Ia at peak brightness. With the model, we can examine how individual SNe vary relative to expectations based on only their light-curve shape. Doing this, we confirm an excess of flux for SN 2011fe at short wavelengths, consistent with its progenitor having a subsolar metallicity. While most other SNe Ia do not show large deviations from the model, ASASSN-14lp has a deficit of flux at short wavelengths, suggesting that its progenitor was relatively metal rich.Comment: 9 pages, 6 figures, submitted to MNRA

CT Automated Exposure Control Using A Generalized Detectability Index

Purpose Identifying an appropriate tube current setting can be challenging when using iterative reconstruction due to the varying relationship between spatial resolution, contrast, noise, and dose across different algorithms. This study developed and investigated the application of a generalized detectability index (d\u27gen) to determine the noise parameter to input to existing automated exposure control (AEC) systems to provide consistent image quality (IQ) across different reconstruction approaches. Methods This study proposes a task‐based automated exposure control (AEC) method using a generalized detectability index (d\u27gen). The proposed method leverages existing AEC methods that are based on a prescribed noise level. The generalized d\u27gen metric is calculated using lookup tables of task‐based modulation transfer function (MTF) and noise power spectrum (NPS). To generate the lookup tables, the American College of Radiology CT accreditation phantom was scanned on a multidetector CT scanner (Revolution CT, GE Healthcare) at 120 kV and tube current varied manually from 20 to 240 mAs. Images were reconstructed using a reference reconstruction algorithm and four levels of an in‐house iterative reconstruction algorithm with different regularization strengths (IR1–IR4). The task‐based MTF and NPS were estimated from the measured images to create lookup tables of scaling factors that convert between d\u27gen and noise standard deviation. The performance of the proposed d\u27gen‐AEC method in providing a desired IQ level over a range of iterative reconstruction algorithms was evaluated using the American College of Radiology (ACR) phantom with elliptical shell and using a human reader evaluation on anthropomorphic phantom images. Results The study of the ACR phantom with elliptical shell demonstrated reasonable agreement between the d\u27gen predicted by the lookup table and d\u27 measured in the images, with a mean absolute error of 15% across all dose levels and maximum error of 45% at the lowest dose level with the elliptical shell. For the anthropomorphic phantom study, the mean reader scores for images resulting from the d\u27gen‐AEC method were 3.3 (reference image), 3.5 (IR1), 3.6 (IR2), 3.5 (IR3), and 2.2 (IR4). When using the d\u27gen‐AEC method, the observers’ IQ scores for the reference reconstruction were statistical equivalent to the scores for IR1, IR2, and IR3 iterative reconstructions (P \u3e 0.35). The d\u27gen‐AEC method achieved this equivalent IQ at lower dose for the IR scans compared to the reference scans. Conclusions A novel AEC method, based on a generalized detectability index, was investigated. The proposed method can be used with some existing AEC systems to derive the tube current profile for iterative reconstruction algorithms. The results provide preliminary evidence that the proposed d\u27gen‐AEC can produce similar IQ across different iterative reconstruction approaches at different dose levels

Low Carbon Abundance in Type Ia Supernovae

We investigate the quantity and composition of unburned material in the outer layers of three normal Type Ia supernovae (SNe Ia): 2000dn, 2002cr and 20 04bw. Pristine matter from a white dwarf progenitor is expected to be a mixture of oxygen and carbon in approximately equal abundance. Using near-infrared (NIR, 0.7-2.5 microns) spectra, we find that oxygen is abundant while carbon is severely depleted with low upper limits in the outer third of the ejected mass. Strong features from the OI line at rest wavelength = 0.7773 microns are observed through a wide range of expansion velocities approx. 9,000 - 18,000 km/s. This large velocity domain corresponds to a physical region of the supernova with a large radial depth. We show that the ionization of C and O will be substantially the same in this region. CI lines in the NIR are expected to be 7-50 times stronger than those from OI but there is only marginal evidence of CI in the spectra and none of CII. We deduce that for these three normal SNe Ia, oxygen is more abundant than carbon by factors of 100 - 1,000. MgII is also detected in a velocity range similar to that of OI. The presence of O and Mg combined with the absence of C indicates that for these SNe Ia, nuclear burning has reached all but the extreme outer layers; any unburned material must have expansion velocities greater than 18,000 km/s. This result favors deflagration to detonation transition (DD) models over pure deflagration models for SNe Ia.Comment: accepted for publication in Ap

Identification of Electron Donor States in N-doped Carbon Nanotubes

Nitrogen doped carbon nanotubes have been synthesized using pyrolysis and characterized by Scanning Tunneling Spectroscopy and transmission electron microscopy. The doped nanotubes are all metallic and exhibit strong electron donor states near the Fermi level. Using tight-binding and ab initio calculations, we observe that pyridine-like N structures are responsible for the metallic behavior and the prominent features near the Fermi level. These electron rich structures are the first example of n-type nanotubes, which could pave the way to real molecular hetero-junction devices.Comment: 5 pages, 4 figures, revtex, submitted to PR

Fractal Dimensions in Perceptual Color Space: A Comparison Study Using Jackson Pollock's Art

The fractal dimensions of color-specific paint patterns in various Jackson Pollock paintings are calculated using a filtering process which models perceptual response to color differences (\Lab color space). The advantage of the \Lab space filtering method over traditional RGB spaces is that the former is a perceptually-uniform (metric) space, leading to a more consistent definition of ``perceptually different'' colors. It is determined that the RGB filtering method underestimates the perceived fractal dimension of lighter colored patterns but not of darker ones, if the same selection criteria is applied to each. Implications of the findings to Fechner's 'Principle of the Aesthetic Middle' and Berlyne's work on perception of complexity are discussed.Comment: 21 pp LaTeX; two postscript figure