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Voids possess a very complex internal structure and dynamics. Using $N$-body simulations we study the hierarchical nature of sub-structures present in the cosmic web (CW). We use the SpineWeb method which provides a complete characterization of the CW into its primary constituents: voids, walls, filaments, and nodes. We aim to characterize the inner compositions of voids by detecting their internal filamentary structure and explore the impact of this on the properties of void galaxies. Using a semi-analytical galaxy evolution model we explore the impact of the CW on several galaxies' properties. We find the fraction of haloes living in various CW components to be a function of their mass, with the majority of the haloes of mass below $10^{12}M_{\odot}/h$, residing in voids and haloes of higher masses distributed mostly in walls. Similarly, in the Stellar-to-Halo mass relationship, we observe an environmental dependence for haloes of masses below $10^{12}M_{\odot}/h$, showing an increased stellar mass fraction for the densest environments. The spin is lower for galaxies in the densest environments for the mass range of $10^{10}-10^{12}M_{\odot}/h$. Finally, we found a strong trend of higher metallicity fractions for filaments and node galaxies, with respect to the full sample, in the range of $M_*<10^{10}M_{\odot}/h$. Our results show that cosmic voids possess an intricate internal network of substructures. This in turn makes them a complex environment for galaxy formation, impacting in an unique way the properties and evolution of the chosen few galaxies that form inside them., Comment: 11 pages, 8 figures

We propose a novel composite framework to find unknown fields in the context of inverse problems for partial differential equations (PDEs). We blend the high expressibility of deep neural networks as universal function estimators with the accuracy and reliability of existing numerical algorithms for partial differential equations as custom layers in semantic autoencoders. Our design brings together techniques of computational mathematics, machine learning and pattern recognition under one umbrella to incorporate domain-specific knowledge and physical constraints to discover the underlying hidden fields. The network is explicitly aware of the governing physics through a hard-coded PDE solver layer in contrast to most existing methods that incorporate the governing equations in the loss function or rely on trainable convolutional layers to discover proper discretizations from data. This subsequently focuses the computational load to only the discovery of the hidden fields and therefore is more data efficient. We call this architecture Blended inverse-PDE networks (hereby dubbed BiPDE networks) and demonstrate its applicability for recovering the variable diffusion coefficient in Poisson problems in one and two spatial dimensions, as well as the diffusion coefficient in the time-dependent and nonlinear Burgers' equation in one dimension. We also show that this approach is robust to noise., Comment: 39 pages, 17 figures

[abridged] We present a detailed comparison of fundamental dark matter halo properties retrieved by a substantial number of different halo finders. These codes span a wide range of techniques including friends-of-friends (FOF), spherical-overdensity (SO) and phase-space based algorithms. We further introduce a robust (and publicly available) suite of test scenarios that allows halo finder developers to compare the performance of their codes against those presented here. This set includes mock haloes containing various levels and distributions of substructure at a range of resolutions as well as a cosmological simulation of the large-scale structure of the universe. All the halo finding codes tested could successfully recover the spatial location of our mock haloes. They further returned lists of particles (potentially) belonging to the object that led to coinciding values for the maximum of the circular velocity profile and the radius where it is reached. All the finders based in configuration space struggled to recover substructure that was located close to the centre of the host halo and the radial dependence of the mass recovered varies from finder to finder. Those finders based in phase space could resolve central substructure although they found difficulties in accurately recovering its properties. Via a resolution study we found that most of the finders could not reliably recover substructure containing fewer than 30-40 particles. However, also here the phase space finders excelled by resolving substructure down to 10-20 particles. By comparing the halo finders using a high resolution cosmological volume we found that they agree remarkably well on fundamental properties of astrophysical significance (e.g. mass, position, velocity, and peak of the rotation curve)., Comment: 27 interesting pages, 20 beautiful figures, and 4 informative tables accepted for publication in MNRAS. The high-resolution version of the paper as well as all the test cases and analysis can be found at the web site http://popia.ft.uam.es/HaloesGoingMAD