Related papers: How to Plant a Merger Tree
Theoretical models are vital for exploring the galaxy merger process, which plays a crucial role in the evolution of galaxies. Recent advances in modelling have placed tight constraints on the buildup of stellar material in galaxies across…
One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…
The mass assembly history (MAH) of dark matter halos plays a crucial role in shaping the formation and evolution of galaxies. MAHs are used extensively in semi-analytic and empirical models of galaxy formation, yet current analytic methods…
We construct an analytic formalism for the mass function of cold dark matter halos, assuming that there is a break in the hierarchical merging process. According to this {\it broken-hierarchy} scenario, due to the inherent nature of the…
We present a new Monte Carlo scheme for the efficient simulation of multi-polymer systems. The method permits chains to be inserted into the system using a biased growth technique. The growth proceeds via the use of a retractable feeler,…
We define some new sequences of recursively constructed random combinatorial trees, and show that, after properly rescaling graph distance and equipping the trees with the uniform measure on vertices, each sequence converges almost surely…
Analytic models based on spherical and ellipsoidal gravitational collapse have been used to derive the mass functions of dark matter halos and their progenitors (the conditional mass function). The ellipsoidal model generally provides a…
The hierarchical growth of dark matter haloes, in which galaxies are hosted, has been studied and modeled using various approaches. In this paper we use a modified version the Sheth & Lemson algorithm for a $\mathrm{\Lambda}$ cold dark…
Supermassive black holes are prevalent at the centers of massive galaxies, and their masses scale with galaxy properties, increasing evidence suggesting that these trends continue to low stellar masses. Seeds are needed for supermassive…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
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…
We introduce an algorithm to generate (not solve) spin-glass instances with planted solutions of arbitrary size and structure. First, a set of small problem patches with open boundaries is solved either exactly or with a heuristic, and then…
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 develop a parametrised model to describe the formation and evolution of massive black holes, designed for comparisons with both electromagnetic and gravitational wave observations. Using an extended Press-Schechter formalism, we generate…
Evolution in the merger rate as a function of redshift is in principle the key observable testing hierarchical models for the formation and evolution of galaxies. However, in practice, direct measurement of this quantity has proven…
We consider the reconciliation problem, in which the task is to find a mapping of a gene tree into a species tree, so as to maximize the likelihood of such fitting, given the available data. We describe a model for the evolution of the…
Divide-and-conquer MCMC is a strategy for parallelising Markov Chain Monte Carlo sampling by running independent samplers on disjoint subsets of a dataset and merging their output. An ongoing challenge in the literature is to efficiently…
The typical problem in Data Science is creating a structure that encodes the occurrence frequency of unique elements in rows and relations between different rows of a data frame. We present the probability tree abstract data structure, an…
We construct a stationary random tree, embedded in the upper half plane, with prescribed offspring distribution and whose vertices are the atoms of a unit Poisson point process. This process which we call Hammersley's tree process extends…
We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. This model…