Related papers: Determining Geodesic Distance on Arbitrary-order S…

In this paper we investigate the use of staged tree models for discrete longitudinal data. Staged trees are a type of probabilistic graphical model for finite sample space processes. They are a natural fit for longitudinal data because a…

Let G be a vertex transitive graph. A study of the range of simple random walk on G and of its bridge is proposed. While it is expected that on a graph of polynomial growth the sizes of the range of the unrestricted random walk and of its…

Graphical model learning and inference are often performed using Bayesian techniques. In particular, learning is usually performed in two separate steps. First, the graph structure is learned from the data; then the parameters of the model…

We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…

We give an elementary proof that Talagrand's sub-Gaussian concentration inequality implies a limit shape theorem for first passage percolation on any Cayley graph of Z^d, with a bound on the speed of convergence that slightly improves…

Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the…

Many machine learning tools for regression are based on recursive partitioning of the covariate space into smaller regions, where the regression function can be estimated locally. Among these, regression trees and their ensembles have…

This contribution is the chapter 2 of the book "geodetic time series analysis" (10.1007/978-3-030-21718-1). The book is dedicated to the art of fitting a trajectory model to those geodetic time series in order to extract accurate…

Stochastic models of diffusion are routinely used to study dispersal of populations, including populations of animals, plants, seeds and cells. Advances in imaging and field measurement technologies mean that data are often collected across…

The reliability of a phylogenetic inference method from genomic sequence data is ensured by its statistical consistency. Bayesian inference methods produce a sample of phylogenetic trees from the posterior distribution given sequence data.…

Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a…

Phylogenetic inference, grounded in molecular evolution models, is essential for understanding the evolutionary relationships in biological data. Accounting for the uncertainty of phylogenetic tree variables, which include tree topologies…

Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…

In route selection problems, the driver's personal preferences will determine whether she prefers a route with a travel time that has a relatively low mean and high variance over one that has relatively high mean and low variance. In…

Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and…

We give algorithms to compute the Fr\'echet distance of trees and graphs with bounded tree width. Our algorithms run in $O(n^2)$ time for trees of bounded degree, and $O(n^2\sqrt{n \log n})$ time for trees of arbitrary degree. For graphs of…

We interleave sampling based motion planning methods with pruning ideas from minimum spanning tree algorithms to develop a new approach for solving a Multi-Goal Path Finding (MGPF) problem in high dimensional spaces. The approach alternates…

We review the problem of finding paths in Cayley graphs of groups and group actions, using the Rubik's cube as an example, and we list several more examples of significant mathematical interest. We then show how to formulate these problems…

Phylogenetic trees are leaf-labelled trees used to model the evolution of species. In practice it is not uncommon to obtain two topologically distinct trees for the same set of species, and this motivates the use of distance measures to…

We study diffusion with a bias towards a target node in networks. This problem is relevant to efficient routing strategies in emerging communication networks like optical networks. Bias is represented by a probability $p$ of the…