Related papers: The Coarse Geometry of Merger Trees in \Lambda CDM

We develop a Multi-Scale Merge-Split Markov chain on redistricting plans. The chain is designed to be usable as the proposal in a Markov Chain Monte Carlo (MCMC) algorithm. Sampling the space of plans amounts to dividing a graph into a…

In this work we propose a novel method to calculate mean first-passage times (MFPTs) for random walks on graphs, based on a dimensionality reduction technique for Markov State Models, known as local-equilibrium (LE). We show that for a…

We consider the hierarchic tree Random Energy Model with continuous branching and calculate the moments of the corresponding partition function. We establish the multifractal properties of those moments. We derive formulas for the normal…

Hidden Markov Models (HMMs) are powerful tools for modeling sequential data, where the underlying states evolve in a stochastic manner and are only indirectly observable. Traditional HMM approaches are well-established for linear sequences,…

Markov Chain Monte Carlo methods have revolutionised mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have been proposed as an efficient way of…

Tree-size distribution is one of the most investigated subjects in plant population biology. The forestry literature reports that tree-size distribution trajectories vary across different stands and/or species, while the metabolic scaling…

In random walks, the path representation of the Green's function is an infinite sum over the length of path probability density functions (PDFs). Here we derive and solve, in Laplace space, the recursion relation for the n order path PDF…

In this paper, we aim to provide probabilistic and combinatorial insights into tree formulas for the Green function and hitting probabilities of Markov chains on a finite state space. These tree formulas are closely related to loop-erased…

The study of matter fields on an ensemble of random geometries is a difficult problem still in need of new methods and ideas. We will follow a point of view inspired by probability theory techniques that relies on an expansion of the two…

We consider maintaining the contour tree $\mathbb{T}$ of a piecewise-linear triangulation $\mathbb{M}$ that is the graph of a time varying height function $h: \mathbb{R}^2 \rightarrow \mathbb{R}$. We carefully describe the combinatorial…

The implementation of ACACIA, a new algorithm to generate dark matter halo merger trees with the Adaptive Mesh Refinement (AMR) code RAMSES, is presented. The algorithm is fully parallel and based on the Message Passing Interface (MPI). As…

Fine-tuning pretrained models has become a standard pathway to achieve state-of-the-art performance across a wide range of domains, leading to a proliferation of task-specific model variants. As the number of such specialized models…

Let $\mathcal H$ be a finite connected undirected graph and $\mathcal H_{walk}$ be the graph of bi-infinite walks on $\mathcal H$; two such walks $\{x_i\}_{i\in \mathbb Z}$ and $\{y_i\}_{i \in \mathbb Z}$ are said to be adjacent if $x_i$ is…

We study three different random walk models on several two-dimensional lattices by Monte Carlo simulations. One is the usual nearest neighbor random walk. Another is the nearest neighbor random walk which is not allowed to backtrack. The…

The metric space of phylogenetic trees defined by Billera, Holmes, and Vogtmann, which we refer to as BHV space, provides a natural geometric setting for describing collections of trees on the same set of taxa. However, it is sometimes…

We follow the spin vector evolutions of well resolved dark matter haloes (containing more than 300 particles) in merger tree main branches from the Millennium and Millennium-II N-body simulations, from z about 3.3 to z = 0. We find that…

The Szegedy quantum walk is a discrete time quantum walk model which defines a quantum analogue of any Markov chain. The long-term behavior of the quantum walk can be encoded in a matrix called the average mixing matrix, whose columns give…

In this paper we study planar morphs between straight-line planar grid drawings of trees. A morph consists of a sequence of morphing steps, where in a morphing step vertices move along straight-line trajectories at constant speed. We show…

Counting non-isomorphic tree-like multigraphs that include self-loops and multiple edges is an important problem in combinatorial enumeration, with applications in chemical graph theory, polymer science, and network modeling. Traditional…

Hierarchical models of structure formation predict that dark matter halo assembly histories are characterised by episodic mergers and interactions with other haloes. An accurate description of this process will provide insights into the…