Related papers: The Coarse Geometry of Merger Trees in \Lambda CDM
Contour trees offer an abstract representation of the level set topology in scalar fields and are widely used in topological data analysis and visualization. However, applying contour trees to large-scale scientific datasets remains…
In this paper, we present a flexible and probabilistic framework for tracking topological features in time-varying scalar fields using merge trees and partial optimal transport. Merge trees are topological descriptors that record the…
We employ a stochastic approach to probing the origin of the log-normal distributions of halo spin in N-body simulations. After analyzing spin evolution in halo merging trees, it was found that a spin change can be characterized by a…
A merge tree is a fundamental topological structure used to capture the sub-level set (and similarly, super-level set) topology in scalar data analysis. The interleaving distance is a theoretically sound, stable metric for comparing merge…
Efficiently mapping baryonic properties onto dark matter is a major challenge in astrophysics. Although semi-analytic models (SAMs) and hydrodynamical simulations have made impressive advances in reproducing galaxy observables across…
Structure identification in cosmological simulations plays an important role in analysing simulation outputs. The definition of these structures directly impacts the inferred properties derived from these simulations. This paper proposes a…
We investigate several approaches for constructing Monte Carlo realizations of the merging history of virialized dark matter halos (``merger trees'') using the extended Press-Schechter formalism. We describe several unsuccessful methods in…
This paper is a detailled study of the coding of real trees by real valued functions that is motivated by probabilistic problems related to continuum random trees. Indeed it is known since the works of Aldous (1993) and Le Gall (1991) that…
A merge tree is a topological descriptor of a real-valued function. Merge trees are used in visualization and topological data analysis, either directly or as a means to another end: computing a 0-dimensional persistence diagram,…
Consider the space of continuous functions on a geometric tree $X$ whose persistent homology gives rise to a finite generic barcode $D$. We show that there are exactly as many path connected components in this space as there are merge trees…
Various laboratory-based experiments are underway attempting to detect dark matter directly. The event rates and detailed signals expected in these experiments depend on the dark matter phase space distribution on sub-milliparsec scales.…
We introduce a novel halo/galaxy matching technique between two cosmological simulations with different resolutions, which utilizes the positions and masses of halos along their subhalo merger tree. With this tool, we conduct a study of…
In this paper we study several problems concerning the number of homomorphisms of trees. We give an algorithm for the number of homomorphisms from a tree to any graph by the Transfer-matrix method. By using this algorithm and some…
I present results from numerical N-body simulations regarding the effect of merging events on the angular momentum distribution of galactic halos as well as a comparison of halo growth in Press-Schechter vs. N-body methods. A total of six…
In order to study the statistics of the objects with hierarchical merging, we propose the skeleton tree formalism, which can analytically distinguish the episodic merging and the continuous accretion in the mass growth processes. The…
Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of $k$ paths ($k$ is odd) along branches of trees or, equivalently, $k$ loop--erased random walks. Starting and ending points of…
Consider a random walk on a tree $G=(V,E)$. For $v,w \in V$, let the hitting time $H(v,w)$ denote the expected number of steps required for the random walk started at $v$ to reach $w$, and let $\pi_v = \mathrm{deg}(v)/2|E|$ denote the…
Contour trees have been developed to visualize or encode scalar data in imaging technologies and scientific simulations. Contours are defined on a continuous scalar field. For discrete data, a continuous function is first interpolated,…
This paper uses combinatorics and group theory to answer questions about the assembly of icosahedral viral shells. Although the geometric structure of the capsid (shell) is fairly well understood in terms of its constituent subunits, the…
In this paper, we are interested in the mixing behaviour of simple random walks on inhomogeneous directed graphs. We focus our study on the Chung-Lu digraph, which is an inhomogeneous network that generalizes the Erd\H{o}s-R\'enyi digraph.…