Related papers: The Coarse Geometry of Merger Trees in \Lambda CDM
The mutational heterogeneity of tumours can be described with a tree representing the evolutionary history of the tumour. With noisy sequencing data there may be uncertainty in the inferred tree structure, while we may also wish to study…
We examine the reliability of the merger trees generated for the Monte-Carlo modeling of galaxy formation. In particular we focus on the cold gas fraction predicted from the merger trees with different assumptions on the progenitor…
Consider the tesselation of the hyperbolic plane by m-gons, l per vertex. In its 1-skeleton, we compute the growth series of vertices, geodesics, tuples of geodesics with common extremities. We also introduce and enumerate "holly trees", a…
We model the acquisition of spin by dark-matter halos in semi-analytic merger trees. We explore two different algorithms; one in which halo spin is acquired from the orbital angular momentum of merging satellites, and another in which halo…
Merge trees are a powerful tool from topological data analysis that is frequently used to analyze scalar fields. The similarity between two merge trees can be captured by an interleaving: a pair of maps between the trees that jointly…
Decision trees are commonly used predictive models due to their flexibility and interpretability. This paper is directed at quantifying the uncertainty of decision tree predictions by employing a Bayesian inference approach. This is…
We extend the random-walk model of Vitvitska et al. for predicting the spins of dark matter halos from their merger histories. Using updated merger rates, orbital parameter distributions, and N-body constraints we show that this model can…
We developed a new method to extract halo merger rates from the Millennium Simulation. First, by removing superfluous mergers that are artifacts of the FOF halo finder, we find a lower merger rate compared to previous work. The reductions…
There are several interrelated notions of discrete curvature on graphs. Many approaches utilize the optimal transportation metric on its probability simplex or the distance matrix of the graph. In this survey article, we compute formulas…
Comparative analysis of scalar fields is an important problem with various applications including feature-directed visualization and feature tracking in time-varying data. Comparing topological structures that are abstract and succinct…
In this paper, we are concerned with mean hitting time $\langle\mathcal{H}\rangle$ for random walks on recursive growth tree networks that are built based on an arbitrary tree as the seed via implementing various primitive graphic…
An important problem in geometric computing is defining and computing similarity between two geometric shapes, e.g. point sets, curves and surfaces, etc. Important geometric and topological information of many shapes can be captured by…
Modelling the growth histories of specific galaxies often involves generating the entire population of objects that arise in a given cosmology and selecting systems with appropriate properties. This approach is highly inefficient when…
Semi-analytic models are best suited to compare galaxy formation and evolution theories with observations. These models rely heavily on halo merger trees, and their realistic features (i.e., no drastic changes on halo mass or jumps on…
We have constructed the merging history of dark matter halos in a SCDM cosmology, by means of a the {``Merging Cell Model''} (Rodrigues & Thomas 1996). It is based on the linear theory of growth of density fluctuations, and the Top-Hat…
This paper presents a new algorithm for the fast, shared memory, multi-core computation of augmented contour trees on triangulations. In contrast to most existing parallel algorithms our technique computes augmented trees, enabling the full…
We study the topological construction called Mapper in the context of simply connected domains, in particular on images. The Mapper construction can be considered as a generalization for contour, split, and joint trees on simply connected…
(abridged) We study the mass assembly history (MAH) of dark matter haloes. We compare MAHs obtained using (i) merger trees constructed with the extended Press-Schechter (EPS) formalism, (ii) numerical simulations, and (iii) the Lagrangian…
We study the ability of PINOCCHIO (PINpointing Orbit-Crossing Collapsed HIerarchical Objects) to predict the merging histories of dark matter (DM) haloes, comparing the PINOCCHIO predictions with the results of two large N-body simulations…
A mated-CRT map is a random planar map obtained as a discretized mating of correlated continuum random trees. Mated-CRT maps provide a coarse-grained approximation of many other natural random planar map models (e.g., uniform triangulations…