Block-Simultaneous Direction Method of Multipliers: A proximal primal-dual splitting algorithm for nonconvex problems with multiple constraints

We introduce a generalization of the linearized Alternating Direction Method of Multipliers to optimize a real-valued function $f$ of multiple arguments with potentially multiple constraints $g_\circ$ on each of them. The function $f$ may be nonconvex as long as it is convex in every argument, while the constraints $g_\circ$ need to be convex but not smooth. If $f$ is smooth, the proposed Block-Simultaneous Direction Method of Multipliers (bSDMM) can be interpreted as a proximal analog to inexact coordinate descent methods under constraints. Unlike alternative approaches for joint solvers of multiple-constraint problems, we do not require linear operators $L$ of a constraint function $g(L\ \cdot)$ to be invertible or linked between each other. bSDMM is well-suited for a range of optimization problems, in particular for data analysis, where $f$ is the likelihood function of a model and $L$ could be a transformation matrix describing e.g. finite differences or basis transforms. We apply bSDMM to the Non-negative Matrix Factorization task of a hyperspectral unmixing problem and demonstrate convergence and effectiveness of multiple constraints on both matrix factors. The algorithms are implemented in python and released as an open-source package.Comment: 13 pages, 4 figure

First measurement of gravitational lensing by cosmic voids in SDSS

We report the first measurement of the diminutive lensing signal arising from matter underdensities associated with cosmic voids. While undetectable individually, by stacking the weak gravitational shear estimates around 901 voids detected in SDSS DR7 by Sutter et al. (2012a), we find substantial evidence for a depression of the lensing signal compared to the cosmic mean. This depression is most pronounced at the void radius, in agreement with analytical models of void matter profiles. Even with the largest void sample and imaging survey available today, we cannot put useful constraints on the radial dark-matter void profile. We invite independent investigations of our findings by releasing data and analysis code to the public at https://github.com/pmelchior/void-lensingComment: 6 pages, 5 figures, as accepted by MNRA

Parametrising arbitrary galaxy morphologies: potentials and pitfalls

We demonstrate that morphological observables (e.g. steepness of the radial light profile, ellipticity, asymmetry) are intertwined and cannot be measured independently of each other. We present strong arguments in favour of model-based parametrisation schemes, namely reliability assessment, disentanglement of morphological observables, and PSF modelling. Furthermore, we demonstrate that estimates of the concentration and Sersic index obtained from the Zurich Structure & Morphology catalogue are in excellent agreement with theoretical predictions. We also demonstrate that the incautious use of the concentration index for classification purposes can cause a severe loss of the discriminative information contained in a given data sample. Moreover, we show that, for poorly resolved galaxies, concentration index and M_20 suffer from strong discontinuities, i.e. similar morphologies are not necessarily mapped to neighbouring points in the parameter space. This limits the reliability of these parameters for classification purposes. Two-dimensional Sersic profiles accounting for centroid and ellipticity are identified as the currently most reliable parametrisation scheme in the regime of intermediate signal-to-noise ratios and resolutions, where asymmetries and substructures do not play an important role. We argue that basis functions provide good parametrisation schemes in the regimes of high signal-to-noise ratios and resolutions. Concerning Sersic profiles, we show that scale radii cannot be compared directly for profiles of different Sersic indices. Furthermore, we show that parameter spaces are typically highly nonlinear. This implies that significant caution is required when distance-based classificaton methods are used.Comment: 18 pages, 13 figure

Detecting Galaxy-Filament Alignments in the Sloan Digital Sky Survey III

Previous studies have shown the filamentary structures in the cosmic web influence the alignments of nearby galaxies. We study this effect in the LOWZ sample of the Sloan Digital Sky Survey using the "Cosmic Web Reconstruction" filament catalogue. We find that LOWZ galaxies exhibit a small but statistically significant alignment in the direction parallel to the orientation of nearby filaments. This effect is detectable even in the absence of nearby galaxy clusters, which suggests it is an effect from the matter distribution in the filament. A nonparametric regression model suggests that the alignment effect with filaments extends over separations of 30-40 Mpc. We find that galaxies that are bright and early-forming align more strongly with the directions of nearby filaments than those that are faint and late-forming; however, trends with stellar mass are less statistically significant, within the narrow range of stellar mass of this sample.Comment: 14 pages, 13 figures. Accepted to the MNRA

Quantifying galaxy shapes: Sersiclets and beyond

Parametrising galaxy morphologies is a challenging task, e.g., in shear measurements of weak lensing or investigations of galaxy evolution. The huge variety of morphologies requires an approach that is highly flexible, e.g., accounting for azimuthal structure. We revisit the method of sersiclets, where galaxy morphologies are decomposed into basis functions based on the Sersic profile. This approach is justified by the fact that the Sersic profile is the first-order Taylor expansion of any real light profile. We show that sersiclets overcome the modelling failures of shapelets. However, sersiclets implicate an unphysical relation between the steepness of the light profile and the spatial scale of azimuthal structures, which is not obeyed by real galaxy morphologies and can therefore give rise to modelling failures. Moreover, we demonstrate that sersiclets are prone to undersampling, which restricts sersiclet modelling to highly resolved galaxy images. Analysing data from the Great08 challenge, we demonstrate that sersiclets should not be used in weak-lensing studies. We conclude that although the sersiclet approach appears very promising at first glance, it suffers from conceptual and practical problems that severly limit its usefulness. The Sersic profile can be enhanced by higher-order terms in the Taylor expansion, which can drastically improve model reconstructions of galaxy images. If orthonormalised, these higher-order profiles can overcome the problems of sersiclets while preserving their mathematical justification.Comment: 14 pages, 12 figures, 2 tables; accepted by MNRA

Density mapping with weak lensing and phase information

The available probes of the large scale structure in the Universe have distinct properties: galaxies are a high resolution but biased tracer of mass, while weak lensing avoids such biases but, due to low signal-to-noise ratio, has poor resolution. We investigate reconstructing the projected density field using the complementarity of weak lensing and galaxy positions. We propose a maximum-probability reconstruction of the 2D lensing convergence with a likelihood term for shear data and a prior on the Fourier phases constructed from the galaxy positions. By considering only the phases of the galaxy field, we evade the unknown value of the bias and allow it to be calibrated by lensing on a mode-by-mode basis. By applying this method to a realistic simulated galaxy shear catalogue, we find that a weak prior on phases provides a good quality reconstruction down to scales beyond l=1000, far into the noise domain of the lensing signal alone.Comment: 11 pages, 9 figures, published in MNRA

Cosmological constraints from the convergence 1-point probability distribution

We examine the cosmological information available from the 1-point probability distribution (PDF) of the weak-lensing convergence field, utilizing fast L-PICOLA simulations and a Fisher analysis. We find competitive constraints in the $\Omega_m$-$\sigma_8$ plane from the convergence PDF with $188\ arcmin^2$ pixels compared to the cosmic shear power spectrum with an equivalent number of modes ($\ell < 886$). The convergence PDF also partially breaks the degeneracy cosmic shear exhibits in that parameter space. A joint analysis of the convergence PDF and shear 2-point function also reduces the impact of shape measurement systematics, to which the PDF is less susceptible, and improves the total figure of merit by a factor of $2-3$, depending on the level of systematics. Finally, we present a correction factor necessary for calculating the unbiased Fisher information from finite differences using a limited number of cosmological simulations.Comment: 10 pages, 5 figure