120 citations · 423 across the 16 of their papers we have counts for
18 papers
Topological bias: How haloes trace structural patterns in the cosmic web
Raul Bermejo, Georg Wilding, Rien van de Weygaert +3
We trace the connectivity of the cosmic web as defined by haloes in the Planck-Millennium simulation using a persistence and Betti curve analysis. We normalise clustering up to the…
Delaunay triangulations of generalized Bolza surfaces
Matthijs Ebbens, Iordan Iordanov, Monique Teillaud +1
The Bolza surface can be seen as the quotient of the hyperbolic plane, represented by the Poincaré disk model, under the action of the group generated by the hyperbolic isometries…
Minimal Delaunay triangulations of hyperbolic surfaces
Matthijs Ebbens, Hugo Parlier, Gert Vegter
Motivated by recent work on Delaunay triangulations of hyperbolic surfaces, we consider the minimal number of vertices of such triangulations. First, we will show that every hyperb…
Persistent homology of the cosmic web. I: Hierarchical topology in CDM cosmologies
Georg Wilding, Keimpe Nevenzeel, Rien van de Weygaert +5
Using a set of CDM simulations of cosmic structure formation, we study the evolving connectivity and changing topological structure of the cosmic web using state-of-the-art tool…
Isotopic Arrangement of Simple Curves: an Exact Numerical Approach based on Subdivision
Jyh-Ming Lien, Vikram Sharma, Gert Vegter +1
This paper presents the first purely numerical (i.e., non-algebraic) subdivision algorithm for the isotopic approximation of a simple arrangement of curves. The arrangement is "sim…
Stochastic Homology of Gaussian vs. non-Gaussian Random Fields: Graphs towards Betti Numbers and Persistence Diagrams
Job Feldbrugge, Matti van Engelen, Rien van de Weygaert +2
The topology and geometry of random fields - in terms of the Euler characteristic and the Minkowski functionals - has received a lot of attention in the context of the Cosmic Micro…
Topology and Geometry of Gaussian random fields I: on Betti Numbers, Euler characteristic and Minkowski functionals
Pratyush Pranav, Rien van de Weygaert, Gert Vegter +6
This study presents a numerical analysis of the topology of a set of cosmologically interesting three-dimensional Gaussian random fields in terms of their Betti numbers , $β_1…
The Topology of the Cosmic Web in Terms of Persistent Betti Numbers
Pratyush Pranav, Herbert Edelsbrunner, Rien van de Weygaert +4
We introduce a multiscale topological description of the Megaparsec weblike cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describi…
Barycentric coordinate neighbourhoods in Riemannian manifolds
Ramsay Dyer, Gert Vegter, Mathijs Wintraecken
We quantify conditions that ensure that a signed measure on a Riemannian manifold has a well defined centre of mass. We then use this result to quantify the extent of a neighbourho…
Certified Computation of planar Morse-Smale Complexes
Amit Chattopadhyay, Gert Vegter, Chee K. Yap
The Morse-Smale complex is an important tool for global topological analysis in various problems of computational geometry and topology. Algorithms for Morse-Smale complexes have b…
Riemannian simplices and triangulations
Ramsay Dyer, Gert Vegter, Mathijs Wintraecken
We study a natural intrinsic definition of geometric simplices in Riemannian manifolds of arbitrary dimension , and exploit these simplices to obtain criteria for triangulating…
Betti numbers of Gaussian fields
Changbom Park, Pratyush Pranav, Pravabati Chingangbam +6
We present the relation between the genus in cosmology and the Betti numbers for excursion sets of three- and two-dimensional smooth Gaussian random fields, and numerically investi…
Alpha, Betti and the Megaparsec Universe: on the Topology of the Cosmic Web
Rien van de Weygaert, Gert Vegter, Herbert Edelsbrunner +13
We study the topology of the Megaparsec Cosmic Web in terms of the scale-dependent Betti numbers, which formalize the topological information content of the cosmic mass distributio…
Adhesion and the Geometry of the Cosmic Web
Johan Hidding, Rien van de Weygaert, Gert Vegter +1
We present a new way to formulate the geometry of the Cosmic Web in terms of Lagrangian space. The Adhesion model has an ingenious geometric interpretation out of which the spine o…
The Sticky Geometry of the Cosmic Web
Johan Hidding, Rien van de Weygaert, Gert Vegter +2
In this video we highlight the application of Computational Geometry to our understanding of the formation and dynamics of the Cosmic Web. The emergence of this intricate and perva…
Probing Dark Energy with Alpha Shapes and Betti Numbers
Rien van de Weygaert, Pratyush Pranav, Bernard J. T. Jones +8
We introduce a new descriptor of the weblike pattern in the distribution of galaxies and matter: the scale dependent Betti numbers which formalize the topological information conte…
Structural Analysis of the SDSS Cosmic Web I.Nonlinear Density Field Reconstructions
Erwin Platen, Rien van de Weygaert, Bernard J. T. Jones +2
We investigate the ability of three reconstruction techniques to analyze and investigate weblike features and geometries in a discrete distribution of objects. The three methods ar…
Alpha Shape Topology of the Cosmic Web
Rien van de Weygaert, Gert Vegter, Erwin Platen +2
We study the topology of the Megaparsec Cosmic Web on the basis of the Alpha Shapes of the galaxy distribution. The simplicial complexes of the alpha shapes are used to determine t…