The probability distribution for non-Gaussianity estimators constructed from the CMB trispectrum

Considerable recent attention has focussed on the prospects to use the cosmic microwave background (CMB) trispectrum to probe the physics of the early universe. Here we evaluate the probability distribution function (PDF) for the standard estimator tau_nle for the amplitude tau_nl of the CMB trispectrum both for the null-hypothesis (i.e., for Gaussian maps with tau_nl = 0) and for maps with a non-vanishing trispectrum (|tau_nl|>0). We find these PDFs to be highly non-Gaussian in both cases. We also evaluate the variance with which the trispectrum amplitude can be measured, , as a function of its underlying value, tau_nl. We find a strong dependence of this variance on tau_nl. We also find that the variance does not, given the highly non-Gaussian nature of the PDF, effectively characterize the distribution. Detailed knowledge of these PDFs will therefore be imperative in order to properly interpret the implications of any given trispectrum measurement. For example, if a CMB experiment with a maximum multipole of lmax = 1500 (such as the Planck satellite) measures tau_nle = 0 then at the 95% confidence our calculations show that we can conclude tau_nl < 1005; assuming a Gaussian PDF but with the correct tau_nl-dependent variance we would incorrectly conclude tau_nl < 4225; further neglecting the tau_nl-dependence in the variance we would incorrectly conclude tau_nl < 361.Comment: 9 pages, 5 figure

Reproductive biology of carpenter seabream (Argyrozona argyrozona) (Pisces: Sparidae) in a marine protected area

The carpenter seabream (Argyrozona argyrozona) is an endemic South African sparid that comprises an important part of the handline fishery. A three-year study (1998−2000) into its reproductive biology within the Tsitsikamma National Park revealed that these fishes are serial spawning late gonochorists. The size at 50% maturity (L50) was estimated at 292 and 297 mm FL for both females and males, respectively. A likelihood ratio test revealed that there was no significant difference between male and female L50 (P>0.5). Both monthly gonadosomatic indices and macroscopically determined ovarian stages strongly indicate that A. argyrozona within the Tsitsikamma National Park spawn in the astral summer between November and April. The presence of postovulatory follicles (POFs) confirmed a six-month spawning season, and monthly proportions of early (0−6 hour old) POFs showed that spawning frequency was highest (once every 1−2 days) from December to March. Although spawning season was more highly correlated to photoperiod (r = 0.859) than temperature (r = −0.161), the daily proportion of spawning fish was strongly correlated (r= 0.93) to ambient temperature over the range 9−22oC. These results indicate that short-term upwelling events, a strong feature in the Tsitsikamma National Park during summer, may negatively affect carpenter fecundity. Both spawning frequency and duration (i.e., length of spawning season) increased with fish length. As a result of the allometric relationship between annual fecundity and fish mass a 3-kg fish was calculated to produce fivefold more eggs per kilogram of body weight than a fish of 1 kg. In addition to producing more eggs per unit of weight each year, larger fish also produce significantly larger eggs

2003 Pollutant Loads Kings River Near Berryville, Arkansas

An automatic sampler and a USGS gauging station were established in 1998 and water quality sampling was begun in 1999 on the Kings River near Berryville, Arkansas. Continuous stage and discharge measurements and frequent water quality sampling have been used to determine pollutant concentrations and loads in the river. This report presents the results from the sampling and analysis for January 1, 2003 to December 31, 2003

On the Kert\'esz line: Some rigorous bounds

We study the Kert\'esz line of the $q$--state Potts model at (inverse) temperature $\beta$, in presence of an external magnetic field $h$. This line separates two regions of the phase diagram according to the existence or not of an infinite cluster in the Fortuin-Kasteleyn representation of the model. It is known that the Kert\'esz line $h_K (\beta)$ coincides with the line of first order phase transition for small fields when $q$ is large enough. Here we prove that the first order phase transition implies a jump in the density of the infinite cluster, hence the Kert\'esz line remains below the line of first order phase transition. We also analyze the region of large fields and prove, using techniques of stochastic comparisons, that $h_K (\beta)$ equals $\log (q - 1) - \log (\beta - \beta_p)$ to the leading order, as $\beta$ goes to $\beta_p = - \log (1 - p_c)$ where $p_c$ is the threshold for bond percolation.Comment: 11 pages, 1 figur

Recent Surge in Homicides Involving Young Black Males and Guns: Time To Reinvest in Prevention and Crime Control

This review of recent U.S. homicide trends by race of offenders and victims, as well as weapons used, shows a surge in homicides that involve young Black males and guns

The CMB Bispectrum, Trispectrum, non-Gaussianity, and the Cramer-Rao Bound

Minimum-variance estimators for the parameter fnl that quantifies local-model non-Gaussianity can be constructed from the cosmic microwave background (CMB) bispectrum (three-point function) and also from the trispectrum (four-point function). Some have suggested that a comparison between the estimates for the values of fnl from the bispectrum and trispectrum allow a consistency test for the model. But others argue that the saturation of the Cramer-Rao bound by the bispectrum estimator implies that no further information on fnl can be obtained from the trispectrum. Here we elaborate the nature of the correlation between the bispectrum and trispectrum estimators for fnl. We show that the two estimators become statistically independent in the limit of large number of CMB pixels and thus that the trispectrum estimator does indeed provide additional information on fnl beyond that obtained from the bispectrum. We explain how this conclusion is consistent with the Cramer-Rao bound. Our discussion of the Cramer-Rao bound may be of interest to those doing Fisher-matrix parameter-estimation forecasts or data analysis in other areas of physics as well.Comment: 11 pages, 3 figure

Inflationary gravitational-wave background and measurements of the scalar spectral index

Inflation predicts a stochastic background of gravitational waves over a broad range of frequencies, from those accessible with cosmic microwave background (CMB) measurements, to those accessible directly with gravitational-wave detectors, like NASA's Big-Bang Observer (BBO), currently under study. In a previous paper [Phys. Rev. D 73, 023504 (2006)] we connected CMB constraints to the amplitude and tensor spectral tilt of the inflationary gravitational-wave background (IGWB) at BBO frequencies for four classes of models of inflation by directly solving the inflationary equations of motion. Here we extend that analysis by including results obtained in the Wilkinson Microwave Anisotropy Probe third-year data release as well as by considering two additional classes of inflationary models. As often noted in the literature, the recent indication that the primordial density power spectrum has a red spectral index implies (with some caveats) that the amplitude of the IGWB may be large enough to be observable in the CMB polarization. Here we also explore the implications for the direct detection of the IGWB