Submodularity in Batch Active Learning and Survey Problems on Gaussian Random Fields

Many real-world datasets can be represented in the form of a graph whose edge weights designate similarities between instances. A discrete Gaussian random field (GRF) model is a finite-dimensional Gaussian process (GP) whose prior covariance is the inverse of a graph Laplacian. Minimizing the trace of the predictive covariance Sigma (V-optimality) on GRFs has proven successful in batch active learning classification problems with budget constraints. However, its worst-case bound has been missing. We show that the V-optimality on GRFs as a function of the batch query set is submodular and hence its greedy selection algorithm guarantees an (1-1/e) approximation ratio. Moreover, GRF models have the absence-of-suppressor (AofS) condition. For active survey problems, we propose a similar survey criterion which minimizes 1'(Sigma)1. In practice, V-optimality criterion performs better than GPs with mutual information gain criteria and allows nonuniform costs for different nodes

A bias in cosmic shear from galaxy selection: results from ray-tracing simulations

We identify and study a previously unknown systematic effect on cosmic shear measurements, caused by the selection of galaxies used for shape measurement, in particular the rejection of close (blended) galaxy pairs. We use ray-tracing simulations based on the Millennium Simulation and a semi-analytical model of galaxy formation to create realistic galaxy catalogues. From these, we quantify the bias in the shear correlation functions by comparing measurements made from galaxy catalogues with and without removal of close pairs. A likelihood analysis is used to quantify the resulting shift in estimates of cosmological parameters. The filtering of objects with close neighbours (a) changes the redshift distribution of the galaxies used for correlation function measurements, and (b) correlates the number density of sources in the background with the density field in the foreground. This leads to a scale-dependent bias of the correlation function of several percent, translating into biases of cosmological parameters of similar amplitude. This makes this new systematic effect potentially harmful for upcoming and planned cosmic shear surveys. As a remedy, we propose and test a weighting scheme that can significantly reduce the bias.Comment: 9 pages, 9 figures, version accepted for publication in Astronomy & Astrophysic

Recoiling Supermassive Black Hole Escape Velocities from Dark Matter Halos

We simulate recoiling black hole trajectories from $z=20$ to $z=0$ in dark matter halos, quantifying how parameter choices affect escape velocities. These choices include the strength of dynamical friction, the presence of stars and gas, the accelerating expansion of the universe (Hubble acceleration), host halo accretion and motion, and seed black hole mass. $\Lambda$CDM halo accretion increases escape velocities by up to 0.6 dex and significantly shortens return timescales compared to non-accreting cases. Other parameters change orbit damping rates but have subdominant effects on escape velocities; dynamical friction is weak at halo escape velocities, even for extreme parameter values. We present formulae for black hole escape velocities as a function of host halo mass and redshift. Finally, we discuss how these findings affect black hole mass assembly as well as minimum stellar and halo masses necessary to retain supermassive black holes.Comment: 10 pages, 17 figures. Updated to correct a typo (sign error) in fit to escape velocity, for return by z=0 (eq. 19

Analysis of two-point statistics of cosmic shear: III. Covariances of shear measures made easy

In recent years cosmic shear, the weak gravitational lensing effect by the large-scale structure of the Universe, has proven to be one of the observational pillars on which the cosmological concordance model is founded. Several cosmic shear statistics have been developed in order to analyze data from surveys. For the covariances of the prevalent second-order measures we present simple and handy formulae, valid under the assumptions of Gaussian density fluctuations and a simple survey geometry. We also formulate these results in the context of shear tomography, i.e. the inclusion of redshift information, and generalize them to arbitrary data field geometries. We define estimators for the E- and B-mode projected power spectra and show them to be unbiased in the case of Gaussianity and a simple survey geometry. From the covariance of these estimators we demonstrate how to derive covariances of arbitrary combinations of second-order cosmic shear measures. We then recalculate the power spectrum covariance for general survey geometries and examine the bias thereby introduced on the estimators for exemplary configurations. Our results for the covariances are considerably simpler than and analytically shown to be equivalent to the real-space approach presented in the first paper of this series. We find good agreement with other numerical evaluations and confirm the general properties of the covariance matrices. The studies of the specific survey configurations suggest that our simplified covariances may be employed for realistic survey geometries to good approximation.Comment: 15 pages, including 4 figures (Fig. 3 reduced in quality); minor changes, Fig. 4 extended; published in A&

Cosmological constraints from the capture of non-Gaussianity in Weak Lensing data

Weak gravitational lensing has become a common tool to constrain the cosmological model. The majority of the methods to derive constraints on cosmological parameters use second-order statistics of the cosmic shear. Despite their success, second-order statistics are not optimal and degeneracies between some parameters remain. Tighter constraints can be obtained if second-order statistics are combined with a statistic that is efficient to capture non-Gaussianity. In this paper, we search for such a statistical tool and we show that there is additional information to be extracted from statistical analysis of the convergence maps beyond what can be obtained from statistical analysis of the shear field. For this purpose, we have carried out a large number of cosmological simulations along the {\sigma}8-{\Omega}m degeneracy, and we have considered three different statistics commonly used for non-Gaussian features characterization: skewness, kurtosis and peak count. To be able to investigate non-Gaussianity directly in the shear field we have used the aperture mass definition of these three statistics for different scales. Then, the results have been compared with the results obtained with the same statistics estimated in the convergence maps at the same scales. First, we show that shear statistics give similar constraints to those given by convergence statistics, if the same scale is considered. In addition, we find that the peak count statistic is the best to capture non-Gaussianities in the weak lensing field and to break the {\sigma}8-{\Omega}m degeneracy. We show that this statistical analysis should be conducted in the convergence maps: first, because there exist fast algorithms to compute the convergence map for different scales, and secondly because it offers the opportunity to denoise the reconstructed convergence map, which improves non-Gaussian features extraction.Comment: Accepted for publication in MNRAS (11 pages, 5 figures, 9 tables

Combined automotive safety and security pattern engineering approach

Automotive systems will exhibit increased levels of automation as well as ever tighter integration with other vehicles, traffic infrastructure, and cloud services. From safety perspective, this can be perceived as boon or bane - it greatly increases complexity and uncertainty, but at the same time opens up new opportunities for realizing innovative safety functions. Moreover, cybersecurity becomes important as additional concern because attacks are now much more likely and severe. However, there is a lack of experience with security concerns in context of safety engineering in general and in automotive safety departments in particular. To address this problem, we propose a systematic pattern-based approach that interlinks safety and security patterns and provides guidance with respect to selection and combination of both types of patterns in context of system engineering. A combined safety and security pattern engineering workflow is proposed to provide systematic guidance to support non-expert engineers based on best practices. The application of the approach is shown and demonstrated by an automotive case study and different use case scenarios.EC/H2020/692474/EU/Architecture-driven, Multi-concern and Seamless Assurance and Certification of Cyber-Physical Systems/AMASSEC/H2020/737422/EU/Secure COnnected Trustable Things/SCOTTEC/H2020/732242/EU/Dependability Engineering Innovation for CPS - DEIS/DEISBMBF, 01IS16043, Collaborative Embedded Systems (CrESt

A proposal on the galaxy intrinsic alignment self-calibration in weak lensing surveys

The galaxy intrinsic alignment causes the galaxy ellipticity-ellipticity power spectrum between two photometric redshifts to decrease faster with respect to the redshift separation $\Delta z^P$, for fixed mean redshift. This offers a valuable diagnosis on the intrinsic alignment. We show that the distinctive dependences of the GG, II and GI correlations on $\Delta z^P$ over the range |\Delta z^P|\la 0.2 can be understood robustly without strong assumptions on the intrinsic alignment. This allows us to measure the intrinsic alignment within each conventional photo-z bin of typical size \ga 0.2, through lensing tomography of photo-z bin size $\sim 0.01$. Both the statistical and systematical errors in the lensing cosmology can be reduced by this self-calibration technique.Comment: v2: minor revisions. 5 pages, 4 figures. MNRAS letters in pres

Comprehensive Two-Point Analyses of Weak Gravitational Lensing Surveys

We present a framework for analyzing weak gravitational lensing survey data, including lensing and source-density observables, plus spectroscopic redshift calibration data. All two-point observables are predicted in terms of parameters of a perturbed Robertson-Walker metric, making the framework independent of the models for gravity, dark energy, or galaxy properties. For Gaussian fluctuations the 2-point model determines the survey likelihood function and allows Fisher-matrix forecasting. The framework includes nuisance terms for the major systematic errors: shear measurement errors, magnification bias and redshift calibration errors, intrinsic galaxy alignments, and inaccurate theoretical predictions. We propose flexible parameterizations of the many nuisance parameters related to galaxy bias and intrinsic alignment. For the first time we can integrate many different observables and systematic errors into a single analysis. As a first application of this framework, we demonstrate that: uncertainties in power-spectrum theory cause very minor degradation to cosmological information content; nearly all useful information (excepting baryon oscillations) is extracted with ~3 bins per decade of angular scale; and the rate at which galaxy bias varies with redshift substantially influences the strength of cosmological inference. The framework will permit careful study of the interplay between numerous observables, systematic errors, and spectroscopic calibration data for large weak-lensing surveys.Comment: submitted to Ap