Related papers: The Coarse Geometry of Merger Trees in \Lambda CDM
Developing a robust algorithm for automatic individual tree crown (ITC) detection from laser scanning datasets is important for tracking the responses of trees to anthropogenic change. Such approaches allow the size, growth and mortality of…
We study a broad class of random labelled trees in which integer-valued labels evolve along the edges according to increments in $\{-1, 0, 1\}$. These models include e.g. branching random walks, embedded complete and incomplete binary…
In this paper, we consider the Markov-Chain Monte Carlo (MCMC) approach for random sampling of combinatorial objects. The running time of such an algorithm depends on the total mixing time of the underlying Markov chain and is unknown in…
Galaxy formation and evolution models, such as semi-analytic models, are powerful theoretical tools for predicting how galaxies evolve across cosmic time. These models follow the evolution of galaxies based on the halo assembly histories…
In this paper we study geometrical and dynamical properties of codimension one foliations, by exploring a relation between length averages and ball averages of certain group actions. We introduce a new mechanism, which relies on the group…
We study the construction of quasimorphisms on groups acting on trees introduced by Monod and Shalom, that we call median quasimorphisms, and in particular we fully characterise actions on trees that give rise to non-trivial median…
Using a mapping of compact polymers on the Manhattan lattice to spanning trees, we calculate exactly the average number of bends at infinite temperature. We then find, in a high temperature approximation, the energy of the system as a…
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…
We show how a Monte Carlo method for generating self-avoiding walks on lattice geometries which employs a binary-tree data structure can be adapted for hard-sphere polymers with continuous degrees of freedom. Data suggests that the time per…
Random walks on bounded degree expander graphs have numerous applications, both in theoretical and practical computational problems. A key property of these walks is that they converge rapidly to their stationary distribution. In this work…
Specifying a full Bayesian model that integrates multiple data sources can be challenging. One natural approach is to specify each individual model separately and join them afterwards. This is the approach adopted in Markov melding.…
We propose a common terminology for use in describing both temporal merger trees and spatial structure trees for dark-matter halos. We specify a unified data format in HDF5 and provide example I/O routines in C, FORTRAN and PYTHON.
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram…
High-resolution N-body simulations of hierarchical clustering in a wide variety of cosmogonies show that the density profiles of dark matter halos are universal, with low mass halos being denser than their more massive counterparts. This…
Based on solid theoretical foundations, we present strong evidences that a number of real-life networks, taken from different domains like Internet measurements, biological data, web graphs, social and collaboration networks, exhibit…
We give a generalization to a continuous setting of the classic Markov chain tree Theorem. In particular, we consider an irreducible diffusion process on a metric graph. The unique invariant measure has an atomic component on the vertices…
We destroy a finite tree of size $n$ by cutting its edges one after the other and in uniform random order. Informally, the associated cut-tree describes the genealogy of the connected components created by this destruction process. We…
In this paper we introduce the horizon visibility graph, a simple extension to the popular horizontal visibility graph representation of a time series, and show that it possesses a rigorous mathematical foundation in computational algebraic…
As galaxy formation and evolution over long cosmic time-scales depends to a large degree on the structure of the universe, the assembly history of galaxies is potentially a powerful approach for learning about the universe itself. In this…
We present a new algorithm (PINOCCHIO, PINpointing Orbit-Crossing Collapsed HIerarchical objects) to predict accurately the formation and evolution of individual dark matter haloes in a given realization of an initial linear density field.…