Reconstruction Analysis of Galaxy Redshift Surveys: A Hybrid Reconstruction Method

In reconstruction analysis of galaxy redshift surveys, one works backwards from the observed galaxy distribution to the primordial density field in the same region, then evolves the primordial fluctuations forward in time with an N-body code. This incorporates assumptions about the cosmological parameters, the properties of primordial fluctuations, and the biasing relation between galaxies and mass. These can be tested by comparing the reconstruction to the observed galaxy distribution, and to peculiar velocity data. This paper presents a hybrid reconstruction method that combines the `Gaussianization'' technique of Weinberg(1992) with the dynamical schemes of Nusser & Dekel(1992) and Gramann(1993). We test the method on N-body simulations and on N-body mock catalogs that mimic the depth and geometry of the Point Source Catalog Redshift Survey and the Optical Redshift Survey. This method is more accurate than Gaussianization or dynamical reconstruction alone. Matching the observed morphology of clustering can limit the bias factor b, independent of Omega. Matching the cluster velocity dispersions and z-space distortions of the correlation function xi(s,mu) constrains the parameter beta=Omega^{0.6}/b. Relative to linear or quasi-linear approximations, a fully non-linear reconstruction makes more accurate predictions of xi(s,mu) for a given beta, thus reducing the systematic biases of beta measurements and offering further scope for breaking the degeneracy between Omega and b. It also circumvents the cosmic variance noise that limits conventional analyses of xi(s,mu). It can also improve the determination of Omega and b from joint analyses of redshift & peculiar velocity surveys as it predicts the fully non-linear peculiar velocity distribution at each point in z-space.Comment: 72 pages including 33 figures, submitted to Ap

Gaussianization of LA-ICP-MS features to improve calibration in forensic glass comparison

The forensic comparison of glass aims to compare a glass sample of an unknown source with a control glass sample of a known source. In this work, we use multi-elemental features from Laser Ablation Inductively Coupled Plasma with Mass Spectrometry (LA-ICP-MS) to compute a likelihood ratio. This calculation is a complex procedure that generally requires a probabilistic model including the within-source and betweensource variabilities of the features. Assuming the within-source variability to be normally distributed is a practical premise with the available data. However, the between-source variability is generally assumed to follow a much more complex distribution, typically described with a kernel density function. In this work, instead of modeling distributions with complex densities, we propose the use of simpler models and the introduction of a data pre-processing step consisting on the Gaussianization of the glass features. In this context, to obtain a better fit of the features with the Gaussian model assumptions, we explore the use of different normalization techniques of the LA-ICP-MS glass features, namely marginal Gaussianization based on histogram matching, marginal Gaussianization based on Yeo-Johnson transformation and a more complex joint Gaussianization using normalizing flows. We report an improvement in the performance of the Likelihood Ratios computed with the previously Gaussianized feature vectors, particularly relevant in their calibration, which implies a more reliable forensic glass comparisonThis work has been supported by the Spanish Ministerio de Ciencia e Innovación through grant PID2021-125943OB-I0

On the Convergence Rate of Gaussianization with Random Rotations

Gaussianization is a simple generative model that can be trained without backpropagation. It has shown compelling performance on low dimensional data. As the dimension increases, however, it has been observed that the convergence speed slows down. We show analytically that the number of required layers scales linearly with the dimension for Gaussian input. We argue that this is because the model is unable to capture dependencies between dimensions. Empirically, we find the same linear increase in cost for arbitrary input $p(x)$, but observe favorable scaling for some distributions. We explore potential speed-ups and formulate challenges for further research

Differentiable Gaussianization Layers for Inverse Problems Regularized by Deep Generative Models

Deep generative models such as GANs and normalizing flows are powerful priors. They can regularize inverse problems to reduce ill-posedness and attain high-quality results. However, the latent vector of such deep generative models can fall out of the desired high-dimensional standard Gaussian distribution during an inversion, particularly in the presence of noise in data or inaccurate forward models. In such a case, deep generative models are ineffective in attaining high-fidelity solutions. To address this issue, we propose to reparameterize and Gaussianize the latent vector using novel differentiable data-dependent layers wherein custom operators are defined by solving optimization problems. These proposed layers constrain an inversion to find feasible in-distribution solutions. We tested and validated our technique on three inversion tasks: compressive-sensing MRI, image deblurring, and eikonal tomography (a nonlinear PDE-constrained inverse problem), using two representative deep generative models: StyleGAN2 and Glow, and achieved state-of-the-art results.Comment: 26 pages, 15 figures, 9 table

A halo bias function measured deeply into voids without stochasticity

We study the relationship between dark-matter haloes and matter in the MIP $N$-body simulation ensemble, which allows precision measurements of this relationship, even deeply into voids. What enables this is a lack of discreteness, stochasticity, and exclusion, achieved by averaging over hundreds of possible sets of initial small-scale modes, while holding fixed large-scale modes that give the cosmic web. We find (i) that dark-matter-halo formation is greatly suppressed in voids; there is an exponential downturn at low densities in the otherwise power-law matter-to-halo density bias function. Thus, the rarity of haloes in voids is akin to the rarity of the largest clusters, and their abundance is quite sensitive to cosmological parameters. The exponential downturn appears both in an excursion-set model, and in a model in which fluctuations evolve in voids as in an open universe with an effective $\Omega_m$ proportional to a large-scale density. We also find that (ii) haloes typically populate the average halo-density field in a super-Poisson way, i.e. with a variance exceeding the mean; and (iii) the rank-order-Gaussianized halo and dark-matter fields are impressively similar in Fourier space. We compare both their power spectra and cross-correlation, supporting the conclusion that one is roughly a strictly-increasing mapping of the other. The MIP ensemble especially reveals how halo abundance varies with `environmental' quantities beyond the local matter density; (iv) we find a visual suggestion that at fixed matter density, filaments are more populated by haloes than clusters.Comment: Changed to version accepted by MNRA

Multiscale analysis of the structure of homogeneous rotating turbulence

International audienceThe structure of homogeneous rotating turbulence at moderate Reynolds number is investigated by analyzing the instantaneous statistics of the scale-dependent velocity gradient tensor perceived by a set of four fluid elements equally spaced. The relative orien-tations between dynamical vectors such as vorticity, rate-of-strain eigenframe, and vortex stretching vector, together with their orientations with the rotating frame, are measured by direct numerical simulation at different rotation rates. Measurements are performed in the entire inertial range of scales. The preferential orientation of turbulence with the rotating frame is found to be maximal at the scale of the horizontal large structures of the flow. The relative orientations between dynamical vectors exhibit a continuous and monotonic evolution with scale. Overall, the orientation properties reflect the Gaussianization and two-dimensionalization of turbulence under the effect of rotation. In particular, rotation suppresses some alignment properties valid in isotropic turbulence, which in turn induces a strong decrease of the enstrophy production and strain production rates. These results are found to be valid at all scales