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The $2$-Edge Connected Spanning Subgraph problem (2ECSS) is among the most basic survivable network design problems: given an undirected unweighted graph, find a subgraph with the minimum number of edges which is 2-edge-connected (i.e., it remains connected after the removal of any single edge). This NP-hard problem is well-studied in terms of approximation algorithms. The current-best approximation factor for 2ECSS is $1.3+\varepsilon$ for any constant $\varepsilon >0$ [Garg, Grandoni, Jabal-Ameli'23; Kobayashi,Noguchi'23]. In this paper we present a much simpler $9/7$ approximation algorithm, and a more complex $5/4$ one. Our algorithms are also faster: their running time is $n^{O(1)}$ instead of $n^{O(1/\varepsilon)}$., Comment: 61 pages, 5 figures

Cosmological simulations play a key role in the prediction and understanding of large scale structure formation from initial conditions. We make use of GAN-based Autoencoders (AEs) in an attempt to predict structure evolution within simulations. The AEs are trained on images and cubes issued from respectively 2D and 3D N-body simulations describing the evolution of the dark matter (DM) field. We find that while the AEs can predict structure evolution for 2D simulations of DM fields well, using only the density fields as input, they perform significantly more poorly in similar conditions for 3D simulations. However, additionally providing velocity fields as inputs greatly improves results, with similar predictions regardless of time-difference between input and target., Comment: 11 pages, 11 figures

In the Triangle-Free (Simple) 2-Matching problem we are given an undirected graph $G=(V,E)$. Our goal is to compute a maximum-cardinality $M\subseteq E$ satisfying the following properties: (1) at most two edges of $M$ are incident on each node (i.e., $M$ is a 2-matching) and (2) $M$ does not induce any triangle. In his Ph.D. thesis from 1984, Harvitgsen presents a complex polynomial-time algorithm for this problem, with a very complex analysis. This result was never published in a journal nor reproved in a different way, to the best of our knowledge. In this paper we have a fresh look at this problem and present a simple PTAS for it based on local search. Our PTAS exploits the fact that, as long as the current solution is far enough from the optimum, there exists a short augmenting trail (similar to the maximum matching case)., Comment: 27 pages, 18 figures

The 2-Vertex-Connected Spanning Subgraph problem (2VCSS) is among the most basic NP-hard (Survivable) Network Design problems: we are given an (unweighted) undirected graph $G$. Our goal is to find a subgraph $S$ of $G$ with the minimum number of edges which is $2$-vertex-connected, namely $S$ remains connected after the deletion of an arbitrary node. 2VCSS is well-studied in terms of approximation algorithms, and the current best (polynomial-time) approximation factor is $10/7$ by Heeger and Vygen [SIDMA'17] (improving on earlier results by Khuller and Vishkin [STOC'92] and Garg, Vempala and Singla [SODA'93])., Comment: 33 pages, 20 figures, ICALP 2023

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

In the Submodular Facility Location problem (SFL) we are given a collection of $n$ clients and $m$ facilities in a metric space. A feasible solution consists of an assignment of each client to some facility. For each client, one has to pay the distance to the associated facility. Furthermore, for each facility $f$ to which we assign the subset of clients $S^f$, one has to pay the opening cost $g(S^f)$, where $g(\cdot)$ is a monotone submodular function with $g(\emptyset)=0$. SFL is APX-hard since it includes the classical (metric uncapacitated) Facility Location problem (with uniform facility costs) as a special case. Svitkina and Tardos [SODA'06] gave the current-best $O(\log n)$ approximation algorithm for SFL. The same authors pose the open problem whether SFL admits a constant approximation and provide such an approximation for a very restricted special case of the problem. We make some progress towards the solution of the above open problem by presenting an $O(\log\log n)$ approximation. Our approach is rather flexible and can be easily extended to generalizations and variants of SFL. In more detail, we achieve the same approximation factor for the practically relevant generalizations of SFL where the opening cost of each facility $f$ is of the form $p_f+g(S^f)$ or $w_f\cdot g(S^f)$, where $p_f,w_f \geq 0$ are input values. We also obtain an improved approximation algorithm for the related Universal Stochastic Facility Location problem. In this problem one is given a classical (metric) facility location instance and has to a priori assign each client to some facility. Then a subset of active clients is sampled from some given distribution, and one has to pay (a posteriori) only the connection and opening costs induced by the active clients. The expected opening cost of each facility $f$ can be modelled with a submodular function of the set of clients assigned to $f$., Comment: 24 pages, 1 algorithm, 1 figure

Are there parallels between the furthest reaches of our universe, and the foundations of thought, awareness, perception, and emotion? What are the connections between the webs and structures that define both? What are the differences? "As Above As Below" was an exhibition that examined these questions. It consisted of six artworks, each of them the product of a collaboration that included at least one artist, astrophysicist, and neuroscientist. The installations explored new parallels between intergalactic and neuronal networks through media such as digital projection, virtual reality, and interactive multimedia, and served to illustrate diverse collaboration practices and ways to communicate across very different fields., Comment: In SciArt Magazine, https://www.sciartmagazine.com/collaboration-as-above-as-below.html ; exhibition video https://youtu.be/RM3gDjb3phU ; panel discussion https://youtu.be/qNhtyvPz8yw ; project website https://asaboveasbelow.com/

The coronavirus disease (COVID-19) has claimed the lives of over 350,000 people and infected more than 6 million people worldwide. Several search engines have surfaced to provide researchers with additional tools to find and retrieve information from the rapidly growing corpora on COVID-19. These engines lack extraction and visualization tools necessary to retrieve and interpret complex relations inherent to scientific literature. Moreover, because these engines mainly rely upon semantic information, their ability to capture complex global relationships across documents is limited, which reduces the quality of similarity-based article recommendations for users. In this work, we present the COVID-19 Knowledge Graph (CKG), a heterogeneous graph for extracting and visualizing complex relationships between COVID-19 scientific articles. The CKG combines semantic information with document topological information for the application of similar document retrieval. The CKG is constructed using the latent schema of the data, and then enriched with biomedical entity information extracted from the unstructured text of articles using scalable AWS technologies to form relations in the graph. Finally, we propose a document similarity engine that leverages low-dimensional graph embeddings from the CKG with semantic embeddings for similar article retrieval. Analysis demonstrates the quality of relationships in the CKG and shows that it can be used to uncover meaningful information in COVID-19 scientific articles. The CKG helps power www.cord19.aws and is publicly available.

Matter in the Universe is arranged in a cosmic web, with a filament of matter typically connecting each neighbouring galaxy pair, separated by tens of millions of light-years. A quadrupolar pattern of the spin field around filaments is known to influence the spins of galaxies and haloes near them, but it remains unknown whether filaments themselves spin. Here, we measure dark-matter velocities around filaments in cosmological simulations, finding that matter generally rotates around them, much faster than around a randomly located axis. It also exhibits some coherence along the filament. The net rotational component is comparable to, and often dominant over, the known quadrupolar flow. The evidence of net rotations revises previous emphasis on a quadrupolar spin field around filaments. The full picture of rotation in the cosmic web is more complicated and multiscale than a network of spinning filamentary rods, but we argue that filament rotation is substantial enough to be an essential part of the picture. It is likely that the longest coherently rotating objects in the Universe are filaments. Also, we speculate that this rotation could provide a mechanism to generate or amplify intergalactic magnetic fields in filaments., Comment: MNRAS, in press. Illustrative animation at https://www.youtube.com/watch?v=h1-a-htHAxY

We introduce a method for generating a continuous, mass-conserving and high-order differentiable density field from a discrete point distribution such as particles or halos from an N-body simulation or galaxies from a spectroscopic survey. The method consists on generating an ensemble of point realizations by perturbing the original point set following the geometric constraints imposed by the Delaunay tessellation in the vicinity of each point in the set. By computing the mean field of the ensemble we are able to significantly reduce artifacts arising from the Delaunay tessellation in poorly sampled regions while conserving the features in the point distribution. Our implementation is based on the Delaunay Tessellation Field Estimation (DTFE) method, however other tessellation techniques are possible. The method presented here shares the same advantages of the DTFE method such as self-adaptive scale, mass conservation and continuity, while being able to reconstruct even the faintest structures of the point distribution usually dominated by artifacts in Delaunay-based methods. Additionally, we also present preliminary results of an application of this method to image denoising and artifact removal, highlighting the broad applicability of the technique introduced here., Comment: Submitted to MNRAS

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

Estimating the parameters of a model describing a set of observations using a neural network is in general solved in a supervised way. In cases when we do not have access to the model's true parameters this approach can not be applied. Standard unsupervised learning techniques on the other hand, do not produce meaningful or semantic representations that can be associated to the model's parameters. Here we introduce a self-supervised hybrid network that combines traditional neural network elements with analytic or numerical models which represent a physical process to be learned by the system. Self-supervised learning is achieved by generating an internal representation equivalent to the parameters of the physical model. This semantic representation is used to evaluate the model and compare it to the input data during training. The Semantic Autoencoder architecture described here shares the robustness of neural networks while including an explicit model of the data, learns in an unsupervised way and estimates, by construction, parameters with direct physical interpretation. As an illustrative application we perform unsupervised learning for 2D model fitting of exponential light profiles.

The standard explanation for galaxy spin starts with the tidal-torque theory (TTT), in which an ellipsoidal dark-matter protohalo, which comes to host the galaxy, is torqued up by the tidal gravitational field around it. We discuss a complementary picture, using the relatively familiar velocity field, instead of the tidal field, whose intuitive connection to the surrounding, possibly faraway matter arrangement is more obscure. In this 'spin from primordial inner motions' (SPIM) concept, implicit in TTT derivations but not previously emphasized, the angular momentum from the gravity-sourced velocity field inside a protohalo largely cancels out, but has some excess from the aspherical outskirts. At first, the net spin scales according to linear theory, a sort of comoving conservation of familiar angular momentum. Then, at collapse, it is conserved in physical coordinates. Small haloes are then typically subject to secondary exchanges of angular momentum. The TTT is useful for analytic estimates. But a literal interpretation of the TTT is inaccurate in detail, without some implicit concepts about smoothing of the velocity and tidal fields. This could lead to misconceptions, for those first learning about how galaxies come to spin. Protohaloes are not perfectly ellipsoidal and do not uniformly torque up, as in a naive interpretation of the TTT; their inner velocity fields retain substantial dispersion. Furthermore, quantitatively, given initial conditions and protohalo boundaries, SPIM is more direct and accurate than the TTT to predict halo spins. We also discuss how SPIM applies to rotating filaments, and the relation between halo mass and spin, in which the total spin of a halo can be thought of as a sum of random contributions., Comment: Accepted to OJA (Open Journal of Astrophysics). 3 movies at https://www.youtube.com/playlist?list=PLJxZSP5_6rBmo7Rz8JgnE1eI2bxRGXGCT

We study the effects of the local environmental density and the cosmic web environment (filaments, walls, and voids) on key properties of dark matter halos using the Bolshoi-Planck LCDM cosmological simulation. The z = 0 simulation is analysed into filaments, walls, and voids using the SpineWeb method and also the VIDE package of tools, both of which use the watershed transform. The key halo properties that we study are the specific mass accretion rate, spin parameter, concentration, prolateness, scale factor of the last major merger, and scale factor when the halo had half of its z = 0 mass. For all these properties, we find that there is no discernible difference between the halo properties in filaments, walls, or voids when compared at the same environmental density. As a result, we conclude that environmental density is the core attribute that affects these properties. This conclusion is in line with recent findings that properties of galaxies in redshift surveys are independent of their cosmic web environment at the same environmental density at z ~ 0. We also find that the local web environment of the Milky Way and the Andromeda galaxies near the centre of a cosmic wall does not appear to have any effect on the properties of these galaxies' dark matter halos except for their orientation, although we find that it is rather rare to have such massive halos near the centre of a relatively small cosmic wall., Comment: 23 pages

We present the first application of deep neural networks to the semantic segmentation of cosmological filaments and walls in the Large Scale Structure of the Universe. Our results are based on a deep Convolutional Neural Network (CNN) with a U-Net architecture trained using an existing state-of-the-art manually-guided segmentation method. We successfully trained an tested an U-Net with a Voronoi model and an N-body simulation. The predicted segmentation masks from the Voronoi model have a Dice coefficient of 0.95 and 0.97 for filaments and mask respectively. The predicted segmentation masks from the N-body simulation have a Dice coefficient of 0.78 and 0.72 for walls and filaments respectively. The relatively lower Dice coefficient in the filament mask is the result of filaments that were predicted by the U-Net model but were not present in the original segmentation mask. Our results show that for a well-defined dataset such as the Voronoi model the U-Net has excellent performance. In the case of the N-body dataset the U-Net produced a filament mask of higher quality than the segmentation mask obtained from a state-of-the art method. The U-Net performs better than the method used to train it, being able to find even the tenuous filaments that the manually-guided segmentation failed to identify. The U-Net presented here can process a $512^3$ volume in a few minutes and without the need of complex pre-processing. Deep CNN have great potential as an efficient and accurate analysis tool for the next generation large-volume computer N-body simulations and galaxy surveys., Comment: Submitted to MNRA. More images at www.dataviz.science/research_machinelearning.html

The cosmic web plays a major role in the formation and evolution of galaxies and defines, to a large extent, their properties. However, the relation between galaxies and environment is still not well understood. Here we present a machine learning approach to study imprints of environmental effects on the mass assembly of haloes. We present a galaxy-LSS machine learning classifier based on galaxy properties sensitive to the environment. We then use the classifier to assess the relevance of each property. Correlations between galaxy properties and their cosmic environment can be used to predict galaxy membership to void/wall or filament/cluster with an accuracy of $93\%$. Our study unveils environmental information encoded in properties of haloes not normally considered directly dependent on the cosmic environment such as merger history and complexity. Understanding the physical mechanism by which the cosmic web is imprinted in a halo can lead to significant improvements in galaxy formation models. This is accomplished by extracting features from galaxy properties and merger trees, computing feature scores for each feature and then applying support vector machine to different feature sets. To this end, we have discovered that the shape and depth of the merger tree, formation time and density of the galaxy are strongly associated with the cosmic environment. We describe a significant improvement in the original classification algorithm by performing LU decomposition of the distance matrix computed by the feature vectors and then using the output of the decomposition as input vectors for support vector machine., Comment: Accepted for publication in MNRAS

The cosmic web is one of the most striking features of the distribution of galaxies and dark matter on the largest scales in the Universe. It is composed of dense regions packed full of galaxies, long filamentary bridges, flattened sheets and vast low density voids. The study of the cosmic web has focused primarily on the identification of such features, and on understanding the environmental effects on galaxy formation and halo assembly. As such, a variety of different methods have been devised to classify the cosmic web -- depending on the data at hand, be it numerical simulations, large sky surveys or other. In this paper we bring twelve of these methods together and apply them to the same data set in order to understand how they compare. In general these cosmic web classifiers have been designed with different cosmological goals in mind, and to study different questions. Therefore one would not {\it a priori} expect agreement between different techniques however, many of these methods do converge on the identification of specific features. In this paper we study the agreements and disparities of the different methods. For example, each method finds that knots inhabit higher density regions than filaments, etc. and that voids have the lowest densities. For a given web environment, we find substantial overlap in the density range assigned by each web classification scheme. We also compare classifications on a halo-by-halo basis; for example, we find that 9 of 12 methods classify around a third of group-mass haloes (i.e. $M_{\rm halo}\sim10^{13.5}h^{-1}M_{\odot}$) as being in filaments. Lastly, so that any future cosmic web classification scheme can be compared to the 12 methods used here, we have made all the data used in this paper public., Comment: 24 pages, 8 figures, 2 tables. Submitted to MN. Comments Welcome

We propose the Cosmic Web Detachment (CWD) model, a framework to interpret the star-formation history of galaxies in a cosmological context. The CWD model unifies several starvation mechanisms known to disrupt or stop star formation into one single physical framework. Galaxies begin accreting star-forming gas at early times via a network of primordial filaments, simply related to the pattern of density fluctuations in the initial conditions. But when shell-crossing occurs on intergalactic scales, this pattern is disrupted, and the galaxy detaches from its primordial filaments, ending the accretion of cold gas. We argue that CWD encompasses known external processes halting star formation, such as harassment, strangulation and starvation. On top of these external processes, internal feedback processes such as AGN contribute to stop in star formation as well. By explicitly pointing out the non-linear nature of CWD events we introduce a simple formalism to identify CWD events in N-body simulations. With it we reproduce and explain, in the context of CWD, several observations including downsizing, the cosmic star formation rate history, the galaxy mass-color diagram and the dependence of the fraction of red galaxies with mass and local density., Comment: 20 pages, accepted for publication in OJA. High-res version: http://skysrv.pha.jhu.edu/~miguel/Papers/CWD/ms.pdf

It is well-known that galaxy environment has a fundamental effect in shaping its properties. We study the environmental effects on galaxy evolution, with an emphasis on the environment defined as the local number density of galaxies. The density field is estimated with different estimators (weighted adaptive kernel smoothing, 10$^{th}$ and 5$^{th}$ nearest neighbors, Voronoi and Delaunay tessellation) for a K$_{s}<$24 sample of $\sim$190,000 galaxies in the COSMOS field at 0.1$<$z$<$3.1. The performance of each estimator is evaluated with extensive simulations. We show that overall, there is a good agreement between the estimated density fields using different methods over $\sim$2 dex in overdensity values. However, our simulations show that adaptive kernel and Voronoi tessellation outperform other methods. Using the Voronoi tessellation method, we assign surface densities to a mass complete sample of quiescent and star-forming galaxies out to z$\sim$3. We show that at a fixed stellar mass, the median color of quiescent galaxies does not depend on their host environment out to z$\sim$3. We find that the number and stellar mass density of massive ($>$10$^{11}$M$_{\odot}$) star-forming galaxies have not significantly changed since z$\sim$3, regardless of their environment. However, for massive quiescent systems at lower redshifts (z$\lesssim$1.3), we find a significant evolution in the number and stellar mass densities in denser environments compared to lower density regions. Our results suggest that the relation between stellar mass and local density is more fundamental than the color-density relation and that environment plays a significant role in quenching star formation activity in galaxies at z$\lesssim$1., Comment: 20 pages, 11 figures, main figures 4,5,8 and 10

We introduce NebulOS, a Big Data platform that allows a cluster of Linux machines to be treated as a single computer. With NebulOS, the process of writing a massively parallel program for a datacenter is no more complicated than writing a Python script for a desktop computer. The platform enables most pre-existing data analysis software to be used, as scale, in a datacenter without modification. The shallow learning curve and compatibility with existing software greatly reduces the time required to develop distributed data analysis pipelines. The platform is built upon industry-standard, open-source Big Data technologies, from which it inherits several fault tolerance features. NebulOS enhances these technologies by adding an intuitive user interface, automated task monitoring, and other usability features. We present a summary of the architecture, provide usage examples, and discuss the system's performance scaling., Comment: 15 pages, 13 figures

We present a method, PhotoWeb, for estimating photometric redshifts of individual galaxies, and their equivalent distance, with megaparsec and even sub-megaparsec accuracy using the Cosmic Web as a constraint over photo-z estimates. PhotoWeb redshift errors for individual galaxies are of the order of delta_z = 0.0007, compared to errors of delta_z = 0.02 for current photo-z techniques. The mean redshift error is of the order of 0.00005-0.0004 compared to mean errors in the range delta_z =z 0.001-0.01 for the best available photo-z estimates in the literature. Current photo-z techniques based on the spectral energy distribution of galaxies and projected clustering produce redshift estimates with large errors due to the poor constraining power the galaxy's spectral energy distribution and projected clustering can provide. The Cosmic Web, on the other hand, provides the strongest constraints on the position of galaxies. The network of walls, filaments and voids occupy ~%10 of the volume of the Universe, yet they contain ~%95 of galaxies. The cosmic web, being a cellular system with well-defined boundaries, sets a restricted set of intermittent positions a galaxy can occupy along a given line-of-sight. Using the information in the density field computed from spectroscopic redshifts we can narrow the possible locations of a given galaxy along the line of sight from a single broad probability distribution (from photo-z) to one or a few narrow peaks. Our first results improve previous photo-z errors by more than one order of magnitude allowing sub-megaparsec errors in some cases. Such accurate estimates for tens of millions of galaxies will allow unprecedented galaxy-LSS studies. In this work we apply our technique to the SDSS photo-z galaxy sample and discuss its performance and future improvements., Comment: Final version submitted to MNRAS

Warm dark matter (WDM) has been proposed as an alternative to cold dark matter (CDM), to resolve issues such as the apparent lack of satellites around the Milky Way. Even if WDM is not the answer to observational issues, it is essential to constrain the nature of the dark matter. The effect of WDM on haloes has been extensively studied, but the small-scale initial smoothing in WDM also affects the present-day cosmic web and voids. It suppresses the cosmic "sub-web" inside voids, and the formation of both void haloes and subvoids. In $N$-body simulations run with different assumed WDM masses, we identify voids with the ZOBOV algorithm, and cosmic-web components with the ORIGAMI algorithm. As dark-matter warmth increases (i.e., particle mass decreases), void density minima grow shallower, while void edges change little. Also, the number of subvoids decreases. The density field in voids is particularly insensitive to baryonic physics, so if void density profiles and minima could be measured observationally, they would offer a valuable probe of the nature of dark matter. Furthermore, filaments and walls become cleaner, as the substructures in between have been smoothed out; this leads to a clear, mid-range peak in the density PDF., Comment: MNRAS, in press. Large WDM vs CDM difference at high mass resolution clarified

Voids represent a unique environment for the study of galaxy evolution, as the lower density environment is expected to result in shorter merger histories and slower evolution of galaxies. This provides an ideal opportunity to test theories of galaxy formation and evolution. Imaging of the neutral hydrogen, central in both driving and regulating star formation, directly traces the gas reservoir and can reveal interactions and signs of cold gas accretion. For a new Void Galaxy Survey (VGS), we have carefully selected a sample of 59 galaxies that reside in the deepest underdensities of geometrically identified voids within the SDSS at distances of ~100 Mpc, and pursued deep UV, optical, Halpha, IR, and HI imaging to study in detail the morphology and kinematics of both the stellar and gaseous components. This sample allows us to not only examine the global statistical properties of void galaxies, but also to explore the details of the dynamical properties. We present an overview of the VGS, and highlight key results on the HI content and individually interesting systems. In general, we find that the void galaxies are gas rich, low luminosity, blue disk galaxies, with optical and HI properties that are not unusual for their luminosity and morphology. We see evidence of both ongoing assembly, through the gas dynamics between interacting systems, and significant gas accretion, seen in extended gas disks and kinematic misalignments. The VGS establishes a local reference sample to be used in future HI surveys (CHILES, DINGO, LADUMA) that will directly observe the HI evolution of void galaxies over cosmic time., Comment: 7 pages, 5 figures. Proceedings of IAU Symposium 308 "The Zeldovich Universe: Genesis and Growth of the Cosmic Web", 23-28 June 2014, Tallinn, Estonia

Cellular systems are observed everywhere in nature, from crystal domains in metals, soap froth and cucumber cells to the network of cosmological voids. Surprisingly, despite their disparate scale and origin all cellular systems follow certain scaling laws relating their geometry, topology and dynamics. Using a cosmological N-body simulation we found that the Cosmic Web, the largest known cellular system, follows the same scaling relations seen elsewhere in nature. Our results extend the validity of scaling relations in cellular systems by over 30 orders of magnitude in scale with respect to previous studies. The dynamics of cellular systems can be used to interpret local observations such as the local velocity anomaly as the result of a collapsing void in our cosmic backyard. Moreover, scaling relations depend on the curvature of space, providing an independent measure of geometry., Comment: Submitted, comments welcomed