Euclid preparation. XXVIII. Forecasts for ten different higher-order weak lensing statistics

Recent cosmic shear studies have shown that higher-order statistics (HOS) developed by independent teams now outperform standard two-point estimators in terms of statistical precision thanks to their sensitivity to the non-Gaussian features of large-scale structure. The aim of the Higher-Order Weak Lensing Statistics (HOWLS) project is to assess, compare, and combine the constraining power of ten different HOS on a common set of Euclid-like mocks, derived from N-body simulations. In this first paper of the HOWLS series, we computed the nontomographic (Ω$_{m}$, σ$_{8}$) Fisher information for the one-point probability distribution function, peak counts, Minkowski functionals, Betti numbers, persistent homology Betti numbers and heatmap, and scattering transform coefficients, and we compare them to the shear and convergence two-point correlation functions in the absence of any systematic bias. We also include forecasts for three implementations of higher-order moments, but these cannot be robustly interpreted as the Gaussian likelihood assumption breaks down for these statistics. Taken individually, we find that each HOS outperforms the two-point statistics by a factor of around two in the precision of the forecasts with some variations across statistics and cosmological parameters. When combining all the HOS, this increases to a 4.5 times improvement, highlighting the immense potential of HOS for cosmic shear cosmological analyses with Euclid. The data used in this analysis are publicly released with the paper

Euclid Preparation. XXVIII. Forecasts for ten different higher-order weak lensing statistics

Recent cosmic shear studies have shown that higher-order statistics (HOS) developed by independent teams now outperform standard two-point estimators in terms of statistical precision thanks to their sensitivity to the non-Gaussian features of large-scale structure. The aim of the Higher-Order Weak Lensing Statistics (HOWLS) project is to assess, compare, and combine the constraining power of ten different HOS on a common set of $Euclid$-like mocks, derived from N-body simulations. In this first paper of the HOWLS series, we computed the nontomographic ($\Omega_{\rm m}$, $\sigma_8$) Fisher information for the one-point probability distribution function, peak counts, Minkowski functionals, Betti numbers, persistent homology Betti numbers and heatmap, and scattering transform coefficients, and we compare them to the shear and convergence two-point correlation functions in the absence of any systematic bias. We also include forecasts for three implementations of higher-order moments, but these cannot be robustly interpreted as the Gaussian likelihood assumption breaks down for these statistics. Taken individually, we find that each HOS outperforms the two-point statistics by a factor of around two in the precision of the forecasts with some variations across statistics and cosmological parameters. When combining all the HOS, this increases to a $4.5$ times improvement, highlighting the immense potential of HOS for cosmic shear cosmological analyses with $Euclid$. The data used in this analysis are publicly released with the paper

Euclid Preparation. XXVIII. Forecasts for ten different higher-order weak lensing statistics

Recent cosmic shear studies have shown that higher-order statistics (HOS) developed by independent teams now outperform standard two-point estimators in terms of statistical precision thanks to their sensitivity to the non-Gaussian features of large-scale structure. The aim of the Higher-Order Weak Lensing Statistics (HOWLS) project is to assess, compare, and combine the constraining power of ten different HOS on a common set of $Euclid$-like mocks, derived from N-body simulations. In this first paper of the HOWLS series, we computed the nontomographic ($\Omega_{\rm m}$, $\sigma_8$) Fisher information for the one-point probability distribution function, peak counts, Minkowski functionals, Betti numbers, persistent homology Betti numbers and heatmap, and scattering transform coefficients, and we compare them to the shear and convergence two-point correlation functions in the absence of any systematic bias. We also include forecasts for three implementations of higher-order moments, but these cannot be robustly interpreted as the Gaussian likelihood assumption breaks down for these statistics. Taken individually, we find that each HOS outperforms the two-point statistics by a factor of around two in the precision of the forecasts with some variations across statistics and cosmological parameters. When combining all the HOS, this increases to a $4.5$ times improvement, highlighting the immense potential of HOS for cosmic shear cosmological analyses with $Euclid$. The data used in this analysis are publicly released with the paper.Comment: 33 pages, 24 figures, main results in Fig. 19 & Table 5, version published in A&

Euclid preparation XXVIII. Forecasts for ten different higher-order weak lensing statistics

Recent cosmic shear studies have shown that higher-order statistics (HOS) developed by independent teams now outperform standard two-point estimators in terms of statistical precision thanks to their sensitivity to the non-Gaussian features of large-scale structure. The aim of the Higher-Order Weak Lensing Statistics (HOWLS) project is to assess, compare, and combine the constraining power of ten different HOS on a common set of Euclid-like mocks, derived from N-body simulations. In this first paper of the HOWLS series, we computed the nontomographic (Ωm, σ8) Fisher information for the one-point probability distribution function, peak counts, Minkowski functionals, Betti numbers, persistent homology Betti numbers and heatmap, and scattering transform coefficients, and we compare them to the shear and convergence two-point correlation functions in the absence of any systematic bias. We also include forecasts for three implementations of higher-order moments, but these cannot be robustly interpreted as the Gaussian likelihood assumption breaks down for these statistics. Taken individually, we find that each HOS outperforms the two-point statistics by a factor of around two in the precision of the forecasts with some variations across statistics and cosmological parameters. When combining all the HOS, this increases to a 4.5 times improvement, highlighting the immense potential of HOS for cosmic shear cosmological analyses with Euclid. The data used in this analysis are publicly released with the paper

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Rilievi di Geologia Tecnica in area urbana

VOLUME EDITO DA REGIONE MARCHE-GNDT E INGV; Contiene CD con cartografia geologia tecnic

Going deep with Minkowski functionals of convergence maps

International audienceAims. Stage IV lensing surveys promise to make an unprecedented amount of excellent data available. This will represent a huge leap in terms of quantity and quality and will open the way for the use of novel tools that surpass the standard second-order statistics for probing the high-order properties of the convergence field. Motivated by these considerations, some of us have started a long-term project aiming at using Minkowski functionals (MFs) as complementary and supplementary probes to increase the lensing figure of merit (FoM).Methods. As a second step on this path, we discuss the use of MFs for a survey consisting of a wide total area Atot that is imaged at a limiting magnitude magW and contains a subset of area Adeep, where observations are pushed to a deeper limiting magnitude magD. We present an updated procedure to match the theoretically predicted MFs to the measured MFs, and take the effect of map reconstruction from noisy shear data into account. We validate this renewed method against simulated datasets with different source redshift distributions and total number density, setting these quantities in accordance with the depth of the survey. We can then rely on a Fisher matrix analysis to forecast the improvement in the FoM that is due to the joint use of shear tomography and MFs under different assumptions on (Atot,  Adeep, and magD), and the prior on the MFs nuisance parameters.Results. We find that MFs can provide valuable help in increasing the FoM of the lensing survey when the nuisance parameters are known with non-negligible precision. The possibility of compensating for the loss of FoM through a cut in the multipole range that is probed by shear tomography is even more interesting. This makes the results more robust against uncertainties in the modeling of nonlinearities. This makes MFs a promising tool for increasing the FoM and also protects the constraints on the cosmological parameters mainly from theoretical systematic effects.Key words: gravitational lensing: weak / cosmology: theory / methods: statistica

Critically Examining the Claimed Value of Convolutions over User-Item Embedding Maps for Recommender Systems

In recent years, algorithm research in the area of recommender systems has shifted from matrix factorization techniques and their latent factor models to neural approaches. However, given the proven power of latent factor models, some newer neural approaches incorporate them within more complex network architectures. One specific idea, recently put forward by several researchers, is to consider potential correlations between the latent factors, i.e., embeddings, by applying convolutions over the user-item interaction map. However, contrary to what is claimed in these articles, such interaction maps do not share the properties of images where Convolutional Neural Networks (CNNs) are particularly useful. In this work, we show through analytical considerations and empirical evaluations that the claimed gains reported in the literature cannot be attributed to the ability of CNNs to model embedding correlations, as argued in the original papers. Moreover, additional performance evaluations show that all of the examined recent CNN-based models are outperformed by existing non-neural machine learning techniques or traditional nearest-neighbor approaches. On a more general level, our work points to major methodological issues in recommender systems research