Weak-lensing shear estimates with general adaptive moments, and studies of bias by pixellation, PSF distortions, and noise

In weak gravitational lensing, weighted quadrupole moments of the brightness profile in galaxy images are a common way to estimate gravitational shear. We employ general adaptive moments (GLAM) to study causes of shear bias on a fundamental level and for a practical definition of an image ellipticity. The GLAM ellipticity has useful properties for any chosen weight profile: the weighted ellipticity is identical to that of isophotes of elliptical images, and in absence of noise and pixellation it is always an unbiased estimator of reduced shear. We show that moment-based techniques, adaptive or unweighted, are similar to a model-based approach in the sense that they can be seen as imperfect fit of an elliptical profile to the image. Due to residuals in the fit, moment-based estimates of ellipticities are prone to underfitting bias when inferred from observed images. The estimation is fundamentally limited mainly by pixellation which destroys information on the original, pre-seeing image. We give an optimized estimator for the pre-seeing GLAM ellipticity and quantify its bias for noise-free images. To deal with pixel noise, we consider a Bayesian approach where the posterior of the GLAM ellipticity can be inconsistent with the true ellipticity if we do not properly account for our ignorance about fit residuals. This underfitting bias is S/N-independent but changes with the pre-seeing brightness profile and the correlation or heterogeneity of pixel noise over the post-seeing image. Furthermore, when inferring a constant ellipticity or, more relevantly, constant shear from a source sample with a distribution of intrinsic properties (sizes, centroid positions, intrinsic shapes), an additional, now noise-dependent bias arises towards low S/N if incorrect priors for the intrinsic properties are used. We discuss the origin of this prior bias.Comment: 18 pages; 5 figures; accepted by A&A after major revision, especially of Sect. 3.3 that corrects the previous discussion on the bias by marginalizatio

Switching Costs, Firm Size, and Market Structure

In many markets homogenous goods are sold both by large global firms ("chain stores") and small local firms. Surprisingly, chain stores often charge higher prices. Examples include hotels, airlines, and coffe shops. We provide a simple model that can account for these pricing patterns. In this model, consumers face costs when switching from one supplier to another and change locations with a given probability. Consequently, chain stores insure consumers against switching costs. In equilibrium, chain stores charge higher prices, yet attract more consumers. Profits of local stores and chain stores increase with consumer mobility, but the latter do so faster.Firm size; switching costs; consumer mobility; market structure

Autonomous Fault Detection in Self-Healing Systems using Restricted Boltzmann Machines

Autonomously detecting and recovering from faults is one approach for reducing the operational complexity and costs associated with managing computing environments. We present a novel methodology for autonomously generating investigation leads that help identify systems faults, and extends our previous work in this area by leveraging Restricted Boltzmann Machines (RBMs) and contrastive divergence learning to analyse changes in historical feature data. This allows us to heuristically identify the root cause of a fault, and demonstrate an improvement to the state of the art by showing feature data can be predicted heuristically beyond a single instance to include entire sequences of information.Comment: Published and presented in the 11th IEEE International Conference and Workshops on Engineering of Autonomic and Autonomous Systems (EASe 2014

Inelastic Confinement-Induced Resonances in Low-Dimensional Quantum Systems

A theoretical model is presented describing the confinement-induced resonances observed in the recent loss experiment of Haller et al. [Phys. Rev. Lett. 104, 153203 (2010)]. These resonances originate from possible molecule formation due to the coupling of center-of-mass and relative motion. A corresponding model is verified by ab initio calculations and predicts the resonance positions in 1D as well as in 2D confinement in agreement with the experiment. This resolves the contradiction of the experimental observations to previous theoretical predictions.Comment: 5 pages, 4 figure

The non-Gaussianity of the cosmic shear likelihood - or: How odd is the Chandra Deep Field South?

(abridged) We study the validity of the approximation of a Gaussian cosmic shear likelihood. We estimate the true likelihood for a fiducial cosmological model from a large set of ray-tracing simulations and investigate the impact of non-Gaussianity on cosmological parameter estimation. We investigate how odd the recently reported very low value of $\sigma_8$ really is as derived from the \textit{Chandra} Deep Field South (CDFS) using cosmic shear by taking the non-Gaussianity of the likelihood into account as well as the possibility of biases coming from the way the CDFS was selected. We find that the cosmic shear likelihood is significantly non-Gaussian. This leads to both a shift of the maximum of the posterior distribution and a significantly smaller credible region compared to the Gaussian case. We re-analyse the CDFS cosmic shear data using the non-Gaussian likelihood. Assuming that the CDFS is a random pointing, we find $\sigma_8=0.68_{-0.16}^{+0.09}$ for fixed $\Omega_{\rm m}=0.25$. In a WMAP5-like cosmology, a value equal to or lower than this would be expected in $\approx 5$ of the times. Taking biases into account arising from the way the CDFS was selected, which we model as being dependent on the number of haloes in the CDFS, we obtain $\sigma_8 = 0.71^{+0.10}_{-0.15}$. Combining the CDFS data with the parameter constraints from WMAP5 yields $\Omega_{\rm m} = 0.26^{+0.03}_{-0.02}$ and $\sigma_8 = 0.79^{+0.04}_{-0.03}$ for a flat universe.Comment: 18 pages, 16 figures, accepted for publication in A&A; New Bayesian treatment of field selection bia

Confronting semi-analytic galaxy models with galaxy-matter correlations observed by CFHTLenS

Testing predictions of semi-analytic models of galaxy evolution against observations help to understand the complex processes that shape galaxies. We compare predictions from the Garching and Durham models implemented on the Millennium Run with observations of galaxy-galaxy lensing (GGL) and galaxy-galaxy-galaxy lensing (G3L) for various galaxy samples with stellar masses in the range 0.5 < (M_* / 10^10 M_Sun) < 32 and photometric redshift range 0.2 < z < 0.6 in the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). We find that the predicted GGL and G3L signals are in qualitative agreement with CFHTLenS data. Quantitatively, the models succeed in reproducing the observed signals in the highest stellar mass bin (16 < ( M_* / 10^10 M_Sun) < 32) but show different degrees of tension for the other stellar mass samples. The Durham models are strongly excluded at the 95% confidence level by the observations as they largely over-predict the amplitudes of the GGL and G3L signals, probably because they predict too many satellite galaxies in massive halos.Comment: 9 pages, 8 figures, submitted to A&A. Comments welcom