Related papers: The Coarse Geometry of Merger Trees in \Lambda CDM
In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered connection between the symmetric group and barcodes in general…
In this work we answer an open question asked by Johnson--Scoville. We show that each merge tree is represented by a discrete Morse function on a path. Furthermore, we present explicit constructions for two different but related kinds of…
We describe a semi-analytic model to predict the triaxial shapes of dark matter halos utilizing the sequences of random merging events captured in merger trees to follow the evolution of each halo's energy tensor. When coupled with a simple…
In this work we define a metric structure to compare functions defined on different merge trees. The metric introduced possesses some stability properties, which we illustrate within a standard topological data analysis (TDA) framework, and…
A method for creating a forest of model trees to fit samples of a function defined on images is described in several steps: down-sampling the images, determining a tree's hyperplanes, applying convolutions to the hyperplanes to handle small…
We introduce gbpTrees: an algorithm for constructing merger trees from cosmological simulations, designed to identify and correct for pathological cases introduced by errors or ambiguities in the halo finding process. gbpTrees is built upon…
In this paper, we extend the notion of a merge tree to that of a generalized merge tree, a merge tree that includes 1-dimensional cycle birth information. Given a discrete Morse function on a $1$-dimensional regular CW complex, we construct…
Edit distances between merge trees of scalar fields have many applications in scientific visualization, such as ensemble analysis, feature tracking or symmetry detection. In this paper, we propose branch mappings, a novel approach to the…
We construct merger trees based on the extended Press-Schechter theory (EPS) in order to study the merger rates of dark matter haloes over a range of present day mass ($10^{10}M_{\sun}\leq M_0 \leq10^{15}M_{\sun}$), progenitor mass…
A common approach in semi-analytic modeling of galaxy formation is to construct Monte Carlo realizations of merger histories of dark matter halos whose masses are sampled from a halo mass function. Both the mass function itself, and the…
We evaluate the accuracy of semi-analytic merger-trees by comparing them with the merging histories of dark-matter halos in N-body simulations, focusing on the joint distribution of the number of progenitors and their masses. We first…
In this work, we propose trait-based merge trees a generalization of merge trees to feature level sets, targeting the analysis of tensor field or general multi-variate data. For this, we employ the notion of traits defined in attribute…
We introduce a Markov chain for sampling from the uniform distribution on a Riemannian manifold $\mathcal{M}$, which we call the $\textit{geodesic walk}$. We prove that the mixing time of this walk on any manifold with positive sectional…
In this paper, we study merge trees induced by a discrete Morse function on a tree. Given a discrete Morse function, we provide a method to constructing an induced merge tree and define a new notion of equivalence of discrete Morse…
We describe a new methodology to analyze the reionization process in numerical simulations: the chronology and the geometry of reionization is investigated by means of merger histories of individual HII regions. From the merger tree of…
A method of deriving and using merging history trees of dark matter galaxy haloes directly from pure gravity N-body simulations is presented. This combines the full non-linearity of N-body simulations with the flexibility of the…
Splitting trees are those random trees where individuals give birth at constant rate during a lifetime with general distribution, to i.i.d. copies of themselves. The width process of a splitting tree is then a binary, homogeneous…
We present a new approach to study galaxy evolution in a cosmological context. We combine cosmological merger trees and semi-analytic models of galaxy formation to provide the initial conditions for multi-merger hydrodynamic simulations. In…
We use a novel statistical tool, the mark correlation functions (MCFs), to study clustering of galaxy-size halos as a function of their properties and environment in a high-resolution numerical simulation of the LambdaCDM cosmology. We…
Merge trees are a common topological descriptor for data with a hierarchical component, such as terrains and scalar fields. The interleaving distance, in turn, is a common distance for comparing merge trees. However, the interleaving…