Related papers: The Coarse Geometry of Merger Trees in \Lambda CDM
The excursion set approach uses the statistics of the density field smoothed on a wide range of scales, to gain insight into a number of interesting processes in nonlinear structure formation, such as cluster assembly, merging and…
Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…
When following the growth of structure in the Universe, we propose replacing merger trees with merger graphs, in which haloes can both merge and split into separate pieces. We show that this leads to smoother mass growth and eliminates…
Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…
Distances on merge trees facilitate visual comparison of collections of scalar fields. Two desirable properties for these distances to exhibit are 1) the ability to discern between scalar fields which other, less complex topological…
Although a fair amount of work has been devoted to growing Monte-Carlo merger trees which resemble those built from an N-body simulation, comparatively little effort has been invested in quantifying the caveats one necessarily encounters…
We study the growth of dark matter halos in the concordance LCDM cosmology using several N-body simulations of large cosmological volumes. We build merger trees from the Millennium and Millennium-II simulations, covering a range 10^9-10^15…
In this work we study the interleaving distance between merge trees from a combinatorial point of view. We use a particular type of matching between trees to obtain a novel formulation of the distance. With such formulation, we tackle the…
In scientific visualization, scalar fields are often compared through edit distances between their merge trees. Typical tasks include ensemble analysis, feature tracking and symmetry or periodicity detection. Tree edit distances represent…
We have used merger trees realizations to study the formation of dark matter haloes. The construction of merger-trees is based on three different pictures about the formation of structures in the Universe. These pictures include: the…
In the $\Lambda$CDM universe, structure formation is generally not a self-similar process, while some self-similarity remains in certain statistics which can greatly simplify our description and understanding of the cosmic structures. In…
Merger trees track the evolution of halos across multiple snapshots. They assign for halos of a particular snapshot, the set of halos from previous snapshots they possibly originated from. In this work, Association rule analysis a well…
A halo merger tree forms the essential backbone of a semi-analytic model for galaxy formation and evolution. Recent studies have pointed out that extracting merger trees from numerical simulations of structure formation is non-trivial;…
The effects of spatial correlations of density fluctuations on merger histories of dark matter haloes (so-called `{\it merger trees}') are analysed. We compare the mass functions of dark haloes derived by a new method for calculating merger…
The merging history of dark matter halos is computed with the Merging Cell Model proposed by Rodrigues & Thomas (1996). While originally discussed in the case of scale-free power spectra, it is developed and tested here in the framework of…
Merger trees track the hierarchical assembly of dark matter halos across cosmic time and serve as essential inputs for semi-analytic models of galaxy formation. However, conventional methods for constructing merger trees rely on ad-hoc…
We study the properties of random walks on complex trees. We observe that the absence of loops reflects in physical observables showing large differences with respect to their looped counterparts. First, both the vertex discovery rate and…
Accurate modeling of galaxy formation in a hierarchical, cold dark matter universe requires the use of sufficiently high-resolution merger trees to obtain convergence in the predicted properties of galaxies. When semi-analytic galaxy…
We construct merger trees of dark matter haloes and quantify their merger rates and mass growth rates using the joint dataset from the Millennium and Millennium-II simulations. The finer resolution of the Millennium-II Simulation has…
Contour trees describe the topology of level sets in scalar fields and are widely used in topological data analysis and visualization. A main challenge of utilizing contour trees for large-scale scientific data is their computation at scale…