Related papers: The Coarse Geometry of Merger Trees in \Lambda CDM
Recognising individual trees within remotely sensed imagery has important applications in forest ecology and management. Several algorithms for tree delineation have been suggested, mostly based on locating local maxima or inverted basins…
In order to study convergences of looptrees, we construct continuum trees and looptrees from real-valued c\`adl\`ag functions without negative jumps called excursions. We then provide a toolbox to manipulate the two resulting codings of…
We offer a unified approach to the theory of concave majorants of random walks by providing a path transformation for a walk of finite length that leaves the law of the walk unchanged whilst providing complete information about the concave…
Consider a stochastic process that behaves as a $d$-dimensional simple and symmetric random walk, except that, with a certain fixed probability, at each step, it chooses instead to jump to a given site with probability proportional to the…
Dark matter subhalos are the remnants of (incomplete) halo mergers. Identifying them and establishing their evolutionary links in the form of merger trees is one of the most important applications of cosmological simulations. The…
The Brownian continuum tree was extensively studied in the 90s as a universal random metric space. One construction obtains the continuum tree by a change of metric from an excursion function (or continuous circle mapping) on $[0,1]$. This…
We study spanning trees on Sierpinski graphs (i.e., finite approximations to the Sierpinski gasket) that are chosen uniformly at random. We construct a joint probability space for uniform spanning trees on every finite Sierpinski graph and…
We develop a time domain random walk approach for conservative solute transport in heterogeneous media where medium properties vary over a distribution of length scales. The spatial transition lengths are equal to the heterogeneity length…
We develop a hybrid galaxy formation model which uses outputs from an N-body simulation to follow the merger histories (or ``merger trees'') of dark matter halos and treats baryonic processes, such as the cooling of gas within halos and…
Feature tracking in time-varying scalar fields is a fundamental task in scientific computing. Topological descriptors, which summarize important features of data, have proved to be viable tools to facilitate this task. The merge tree is a…
We develop a new Markov chain on graph partitions that makes relatively global moves yet is computationally feasible to be used as the proposal in the Metropolis-Hastings method. Our resulting algorithm can be made reversible and able to…
The merging rate of cosmic structures is computed, relying on the Ansatz that they can be predicted in the initial linear density field from the coalescence of critical points with increasing smoothing scale, used here as a proxy for cosmic…
We give a new rapid mixing result for a natural random walk on the independent sets of a graph $G$. We show that when $G$ has bounded treewidth, this random walk -- known as the Glauber dynamics for the hardcore model -- mixes rapidly for…
A six-dimensional parameter space based on high-resolution numerical simulations of isolated binary galaxy collisions has been constructed to investigate the dynamical friction timescales, $\tau_{\rm mer}$, for major mergers. Our…
In this article it is shown that the Brownian motion on the continuum random tree is the scaling limit of the simple random walks on any family of discrete $n$-vertex ordered graph trees whose search-depth functions converge to the Brownian…
In tree based adaptive mesh refinement, elements are partitioned between processes using a space filling curve. The curve establishes an ordering between all elements that derive from the same root element, the tree. When representing more…
This paper is concerned with the continuous-time quantum walk on Z, Z^d, and infinite homogeneous trees. By using the generating function method, we compute the limit of the average probability distribution for the general isotropic walk on…
In this paper we examine the relationship between hyperconvex hulls and metric trees. After providing a linking construction for hyperconvex spaces, we show that the four-point property is inherited by the hyperconvex hull, which leads to…
Galled trees, directed acyclic graphs that model evolutionary histories with isolated hybridization events, have become very popular due to both their biological significance and the existence of polynomial time algorithms for their…
This paper calculates several useful statistical properties of the convex minorant process generated by random walk processes. In particular, we calculate the statistics of the longest segment in the convex minorant of a random walk of a…