Renyi Entropies of Interacting Fermions from Determinantal Quantum Monte Carlo Simulations

Entanglement measures such as the entanglement entropy have become an indispensable tool to identify the fundamental character of ground states of interacting quantum many-body systems. For systems of interacting spin or bosonic degrees of freedom much recent progress has been made not only in the analytical description of their respective entanglement entropies but also in their numerical classification. Systems of interacting fermionic degrees of freedom however have proved to be more difficult to control, in particular with regard to the numerical understanding of their entanglement properties. Here we report a generalization of the replica technique for the calculation of Renyi entropies to the framework of determinantal Quantum Monte Carlo simulations -- the numerical method of choice for unbiased, large-scale simulations of interacting fermionic systems. We demonstrate the strength of this approach over a recent alternative proposal based on a decomposition in free fermion Green's functions by studying the entanglement entropy of one-dimensional Hubbard systems both at zero and finite temperatures.Comment: 11 pages, 10 figure

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

Decline in effectiveness of antenatal corticosteroids with time to birth : real or artefact?

The effectiveness of antenatal corticosteroids to prevent neonatal lung disease in women at risk of preterm birth was established by systematic reviews. In addition, subgroup analyses suggested that treatment was most effective in babies born one to seven days after administration. This belief led to widespread use of repeated courses of corticosteroids in women who did not deliver within a week or two of initial treatment. However, the notion that effectiveness declines after seven days may be incorrect, as the analyses that it is based on are unreliable. Here, we discuss the methodological problems of these analyses and their relevance to current randomised controlled trials of repeated versus single courses

Europe on the Brink

Europe’s efforts to stabilize its finances are failing, and the region needs to prepare for widespread restructuring of sovereign and bank debt. Peter Boone and Simon Johnson argue that Europe’s financial system has relied on a policy of protecting creditors from default and has thus spread pervasive moral hazard—a presumption by creditors that they will not take losses on their loans to Greece and other ailing countries. The authors argue that this situation is no longer tenable and examine three possible scenarios for the coming months as the sovereign debt crisis evolves. Under the first scenario, the euro area would try to reassert its commitment to avoid defaults and inflation. This continuation of the moral hazard regime would require severe austerity for Greece and other countries on the periphery of the euro area. The second scenario involves elimination of the moral hazard regime. The euro area would admit that some sovereigns have too much debt. A series of debt restructurings would follow. The final scenario would be for policymakers to continue to contradict themselves by promising selective defaults or restructurings of some countries’ debts while maintaining that they can ensure the stability of the rest of the euro area. But the authors argue that it is an illusion to believe that selective restructuring would not introduce contagion. Such an approach would result in panic, massive capital flight, and disorderly defaults. The ensuing chaos would in turn lead to a negatively charged political atmosphere that would make consensus nearly impossible.

A bayesian analysis of beta testing

In this article, we define a model for fault detection during the beta testing phase of a software design project. Given sampled data, we illustrate how to estimate the failure rate and the number of faults in the software using Bayesian statistical methods with various different prior distributions. Secondly, given a suitable cost function, we also show how to optimise the duration of a further test period for each one of the prior distribution structures considered