On Recovering the Nonlinear Bias Function from Counts in Cells Measurements

We present a simple and accurate method to constrain galaxy bias based on the distribution of counts in cells. The most unique feature of our technique is that it is applicable to non-linear scales, where both dark matter statistics and the nature of galaxy bias are fairly complex. First, we estimate the underlying continuous distribution function from precise counts-in-cells measurements assuming local Poisson sampling. Then a robust, non-parametric inversion of the bias function is recovered from the comparison of the cumulative distributions in simulated dark matter and galaxy catalogs. Obtaining continuous statistics from the discrete counts is the most delicate novel part of our recipe. It corresponds to a deconvolution of a (Poisson) kernel. For this we present two alternatives: a model independent algorithm based on Richardson-Lucy iteration, and a solution using a parametric skewed lognormal model. We find that the latter is an excellent approximation for the dark matter distribution, but the model independent iterative procedure is more suitable for galaxies. Tests based on high resolution dark matter simulations and corresponding mock galaxy catalogs show that we can reconstruct the non-linear bias function down to highly non-linear scales with high precision in the range of $-1 \le \delta \le 5$. As far as the stochasticity of the bias, we have found a remarkably simple and accurate formula based on Poisson noise, which provides an excellent approximation for the scatter around the mean non-linear bias function. In addition we have found that redshift distortions have a negligible effect on our bias reconstruction, therefore our recipe can be safely applied to redshift surveys.Comment: 32 pages, 18 figures; submitted to Ap

Magnification relations of quad lenses and applications on Einstein crosses

In this work, we mainly study the magnification relations of quad lens models for cusp, fold and cross configurations. By dividing and ray-tracing in different image regions, we numerically derive the positions and magnifications of the four images for a point source lying inside of the astroid caustic. Then, based on the magnifications, we calculate the signed cusp and fold relations for the singular isothermal elliptical lenses. The signed fold relation map has positive and negative regions, and the positive region is usually larger than the negative region as has been confirmed before. It can also explain that for many observed fold image pairs, the fluxes of the Fermat minimum images are apt to be larger than those of the saddle images. We define a new quantity cross relation which describes the magnification discrepancy between two minimum images and two saddle images. Distance ratio is also defined as the ratio of the distance of two saddle images to that of two minimum images. We calculate the cross relations and distance ratios for nine observed Einstein crosses. In theory, for most of the quad lens models, the cross relations decrease as the distance ratios increase. In observation, the cross relations of the nine samples do not agree with the quad lens models very well, nevertheless, the cross relations of the nine samples do not give obvious evidence for anomalous flux ratio as the cusp and fold types do. Then, we discuss several reasons for the disagreement, and expect good consistencies for more precise observations and better lens models in the future.Comment: 12 pages, 11 figures, accepted for publication in MNRA

Suppression of low-energy Andreev states by a supercurrent in YBa_2Cu_3O_7-delta

We report a coherence-length scale phenomenon related to how the high-Tc order parameter (OP) evolves under a directly-applied supercurrent. Scanning tunneling spectroscopy was performed on current-carrying YBa_2Cu_3O_7-delta thin-film strips at 4.2K. At current levels well below the theoretical depairing limit, the low-energy Andreev states are suppressed by the supercurrent, while the gap-like structures remain unchanged. We rule out the likelihood of various extrinsic effects, and propose instead a model based on phase fluctuations in the d-wave BTK formalism to explain the suppression. Our results suggest that a supercurrent could weaken the local phase coherence while preserving the pairing amplitude. Other possible scenarios which may cause the observed phenomenon are also discussed.Comment: 6 pages, 4 figures, to appear in Physical Review

Characteristics of Magnetoplasmas Semiannual Status Report No. 12, May 1 - Oct. 31, 1965

Magnetoplasma characteristics - anomalous diffusion across magnetic field, heat conduction in plasma, cesium plasma generator, and electron velocity distribution function in magnetoplasma

Current Path Properties of the Transport Anisotropy at Filling Factor 9/2

To establish the presence and orientation of the proposed striped phase in ultra-high mobility 2D electron systems at filling factor 9/2, current path transport properties are determined by varying the separation and allignment of current and voltage contacts. Contacts alligned orthogonal to the proposed intrinsic striped phase produce voltages consistent with current spreading along the stripes; current driven along the proposed stripe direction results in voltages consistent with channeling along the stripes. Direct comparison is made to current spreading/channeling properties of artificially induced 1D charge modulated systems, which indicates the 9/2 direction.Comment: 10 pages, 4 figure

A New Young Diagrammatic Method For Kronecker Products of O(n) and Sp(2m)

A new simple Young diagrammatic method for Kronecker products of O(n) and Sp(2m) is proposed based on representation theory of Brauer algebras. A general procedure for the decomposition of tensor products of representations for O(n) and Sp(2m) is outlined, which is similar to that for U(n) known as the Littlewood rules together with trace contractions from a Brauer algebra and some modification rules given by King.Comment: Latex, 11 pages, no figure

Cosmological Three-Point Function: Testing The Halo Model Against Simulations

We perform detailed comparison of the semi-analytic halo model predictions with measurements in numerical simulations of the two and three point correlation functions (3PCF), as well as power spectrum and bispectrum. We discuss the accuracy and self-consistency of the halo model description of gravitational clustering in the non-linear regime and constrain halo model parameters. We exploit the recently proposed multipole expansion of three point statistics that expresses rotation invariance in the most natural way. This not only offers technical advantages by reducing the integrals required for the halo model predictions, but amounts to a convenient way of compressing the information contained in the 3PCF. We find that, with an appropriate choice of the halo boundary and mass function cut-off, halo model predictions are in good agreement with the bispectrum measured in numerical simulations. However, the halo model predicts less than the observed configuration dependence of the 3PCF on ~ Mpc scales. This effect is mainly due to quadrupole moment deficit, possibly related to the assumption of spherical halo geometry. Our analysis shows that using its harmonic decomposition, the full configuration dependence of the 3PCF in the non-linear regime can be compressed into just a few numbers, the lowest multipoles. Moreover, these multipoles are closely related to the highest signal to noise eigenmodes of the 3PCF. Therefore this estimator may simplify future analyses aimed at constraining cosmological and halo model parameters from observational data.Comment: Minor corrections. Accepted for publication by Ap

Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm

The primal-dual optimization algorithm developed in Chambolle and Pock (CP), 2011 is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems for the purpose of designing iterative image reconstruction algorithms for CT. The primal-dual algorithm is briefly summarized in the article, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application modeling breast CT with low-intensity X-ray illumination is presented.Comment: Resubmitted to Physics in Medicine and Biology. Text has been modified according to referee comments, and typos in the equations have been correcte