Getting the Measure of the Flatness Problem

The problem of estimating cosmological parameters such as $\Omega$ from noisy or incomplete data is an example of an inverse problem and, as such, generally requires a probablistic approach. We adopt the Bayesian interpretation of probability for such problems and stress the connection between probability and information which this approach makes explicit. This connection is important even when information is ``minimal'' or, in other words, when we need to argue from a state of maximum ignorance. We use the transformation group method of Jaynes to assign minimally--informative prior probability measure for cosmological parameters in the simple example of a dust Friedman model, showing that the usual statements of the cosmological flatness problem are based on an inappropriate choice of prior. We further demonstrate that, in the framework of a classical cosmological model, there is no flatness problem.Comment: 11 pages, submitted to Classical and Quantum Gravity, Tex source file, no figur

Values of H_0 from Models of the Gravitational Lens 0957+561

The lensed double QSO 0957+561 has a well-measured time delay and hence is useful for a global determination of H0. Uncertainty in the mass distribution of the lens is the largest source of uncertainty in the derived H0. We investigate the range of \hn produced by a set of lens models intended to mimic the full range of astrophysically plausible mass distributions, using as constraints the numerous multiply-imaged sources which have been detected. We obtain the first adequate fit to all the observations, but only if we include effects from the galaxy cluster beyond a constant local magnification and shear. Both the lens galaxy and the surrounding cluster must depart from circular symmetry as well. Lens models which are consistent with observations to 95% CL indicate H0=104^{+31}_{-23}(1-\kthirty) km/s/Mpc. Previous weak lensing measurements constrain the mean mass density within 30" of G1 to be kthirty=0.26+/-0.16 (95% CL), implying H0=77^{+29}_{-24}km/s/Mpc (95% CL). The best-fitting models span the range 65--80 km/s/Mpc. Further observations will shrink the confidence interval for both the mass model and \kthirty. The range of H0 allowed by the full gamut of our lens models is substantially larger than that implied by limiting consideration to simple power law density profiles. We therefore caution against use of simple isothermal or power-law mass models in the derivation of H0 from other time-delay systems. High-S/N imaging of multiple or extended lensed features will greatly reduce the H0 uncertainties when fitting complex models to time-delay lenses.Comment: AASTEX, 48 pages 4 figures, 2 tables. Also available at: http://www.astro.lsa.umich.edu:80/users/philf/www/papers/list.htm

Previously Unidentified Changes in Renal Cell Carcinoma Gene Expression Identified by Parametric Analysis of Microarray Data

BACKGROUND. Renal cell carcinoma is a common malignancy that often presents as a metastatic-disease for which there are no effective treatments. To gain insights into the mechanism of renal cell carcinogenesis, a number of genome-wide expression profiling studies have been performed. Surprisingly, there is very poor agreement among these studies as to which genes are differentially regulated. To better understand this lack of agreement we profiled renal cell tumor gene expression using genome-wide microarrays (45,000 probe sets) and compare our analysis to previous microarray studies. METHODS. We hybridized total RNA isolated from renal cell tumors and adjacent normal tissue to Affymetrix U133A and U133B arrays. We removed samples with technical defects and removed probesets that failed to exhibit sequence-specific hybridization in any of the samples. We detected differential gene expression in the resulting dataset with parametric methods and identified keywords that are overrepresented in the differentially expressed genes with the Fisher-exact test. RESULTS. We identify 1,234 genes that are more than three-fold changed in renal tumors by t-test, 800 of which have not been previously reported to be altered in renal cell tumors. Of the only 37 genes that have been identified as being differentially expressed in three or more of five previous microarray studies of renal tumor gene expression, our analysis finds 33 of these genes (89%). A key to the sensitivity and power of our analysis is filtering out defective samples and genes that are not reliably detected. CONCLUSIONS. The widespread use of sample-wise voting schemes for detecting differential expression that do not control for false positives likely account for the poor overlap among previous studies. Among the many genes we identified using parametric methods that were not previously reported as being differentially expressed in renal cell tumors are several oncogenes and tumor suppressor genes that likely play important roles in renal cell carcinogenesis. This highlights the need for rigorous statistical approaches in microarray studies.National Institutes of Healt

Boosting jet power in black hole spacetimes

The extraction of rotational energy from a spinning black hole via the Blandford-Znajek mechanism has long been understood as an important component in models to explain energetic jets from compact astrophysical sources. Here we show more generally that the kinetic energy of the black hole, both rotational and translational, can be tapped, thereby producing even more luminous jets powered by the interaction of the black hole with its surrounding plasma. We study the resulting Poynting jet that arises from single boosted black holes and binary black hole systems. In the latter case, we find that increasing the orbital angular momenta of the system and/or the spins of the individual black holes results in an enhanced Poynting flux.Comment: 7 pages, 5 figure

THE OPTIMAL PLYOMETRIC EXERCISE HORIZONTAL TO VERTICAL FORCE RATIO FOR SPRINTING

This study determined the horizontal to vertical force ratio (H:V) of two types of sprint starts and a variety of plyometric exercise, for the purpose of determining the exercises which are most biomechanically specific to sprinting. Subjects included 15 men. All subjects’ performed the sprinter start, the standing sprint start, the CMJ, 18 inch hurdle hop, bounding, power skipping, standing long jump, and multiple hops, starting on a force platform. A repeated measures ANOVA was used to determine differences in H:V between the sprinter start, the standing start, and the plyometric exercises. Results reveal significant main effects for sprint start H:V and standing start H:V, and the plyometric exercises H:V (p ≤ 0.001). Post-hoc analyses revealed that bounding and standing long jumps are the most biomechanically for training athletes for sprint starts

Bound states of magnons in the S=1/2 quantum spin ladder

We study the excitation spectrum of the two-leg antiferromagnetic S=1/2 Heisenberg ladder. Our approach is based on the description of the excitations as triplets above a strong-coupling singlet ground state. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. We find singlet (S=0) and triplet (S=1) two-particle bound states of the elementary triplets. We argue that bound states generally exist in any dimerized quantum spin model.Comment: 4 REVTeX pages, 4 Postscript figure

Nowhere to Hide: Radio-faint AGN in the GOODS-N field. I. Initial catalogue and radio properties

(Abridged) Conventional radio surveys of deep fields ordinarily have arc-second scale resolutions often insufficient to reliably separate radio emission in distant galaxies originating from star-formation and AGN-related activity. Very long baseline interferometry (VLBI) can offer a solution by identifying only the most compact radio emitting regions in galaxies at cosmological distances where the high brightness temperatures (in excess of $10^5$ K) can only be reliably attributed to AGN activity. We present the first in a series of papers exploring the faint compact radio population using a new wide-field VLBI survey of the GOODS-N field. The unparalleled sensitivity of the European VLBI Network (EVN) will probe a luminosity range rarely seen in deep wide-field VLBI observations, thus providing insights into the role of AGN to radio luminosities of the order $10^{22}~\mathrm{W\,Hz^{-1}}$ across cosmic time. The newest VLBI techniques are used to completely cover an entire 7'.5 radius area to milliarcsecond resolutions, while bright radio sources ($S > 0.1$ mJy) are targeted up to 25 arcmin from the pointing centre. Multi-source self-calibration, and a primary beam model for the EVN array are used to correct for residual phase errors and primary beam attenuation respectively. This paper presents the largest catalogue of VLBI detected sources in GOODS-N comprising of 31 compact radio sources across a redshift range of 0.11-3.44, almost three times more than previous VLBI surveys in this field. We provide a machine-readable catalogue and introduce the radio properties of the detected sources using complementary data from the e-MERLIN Galaxy Evolution survey (eMERGE).Comment: 15 pages, 8 figures, accepted in A&A. Machine-readable table available upon reques

Fast calculation of a family of elliptical mass gravitational lens models

Because of their simplicity, axisymmetric mass distributions are often used to model gravitational lenses. Since galaxies are usually observed to have elliptical light distributions, mass distributions with elliptical density contours offer more general and realistic lens models. They are difficult to use, however, since previous studies have shown that the deflection angle (and magnification) in this case can only be obtained by rather expensive numerical integrations. We present a family of lens models for which the deflection can be calculated to high relative accuracy (one part in 100000) with a greatly reduced numerical effort, for small and large ellipticity alike. This makes it easier to use these distributions for modelling individual lenses as well as for applications requiring larger computing times, such as statistical lensing studies. A program implementing this method can be obtained from the author (or at http://www.sns.ias.edu/~barkana/ellip.html).Comment: 13 pages, 3 figures, submitted to ApJ, also available at http://www.sns.ias.edu/~barkana/ellip.htm