Related papers: Distance statistics in large toroidal maps
We define several new models for how to define anomalous regions among enormous sets of trajectories. These are based on spatial scan statistics, and identify a geometric region which captures a subset of trajectories which are…
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…
This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…
Loss tomography has received considerable attention in recent years and a number of estimators based on maximum likelihood (ML) or Bayesian principles have been proposed. Almost all of the estimators are devoted to the tree topology despite…
We formulate and solve a regression problem with time-stamped distributional data. Distributions are considered as points in the Wasserstein space of probability measures, metrized by the 2-Wasserstein metric, and may represent images,…
We study simple random walk on the uniform spanning tree on Z^2 . We obtain estimates for the transition probabilities of the random walk, the distance of the walk from its starting point after n steps, and exit times of both Euclidean…
We consider the problem of estimating species trees from unrooted gene tree topologies in the presence of incomplete lineage sorting, a common phenomenon that creates gene tree heterogeneity in multilocus datasets. One popular class of…
We analyze the statistics of the shortest and fastest paths on the road network between randomly sampled end points. To a good approximation, these optimal paths are found to be directed in that their lengths (at large scales) are linearly…
One among several advantages of measure transport methods is that they allow for a unified framework for processing and analysis of data distributed according to a wide class of probability measures. Within this context, we present results…
We consider the probability that a spanning tree chosen uniformly at random from a graph can be partitioned into a fixed number $k$ of trees of equal size by removing $k-1$ edges. In that case, the spanning tree is called {\em splittable}.…
The most widely used internal measure for clustering evaluation is the silhouette coefficient, whose naive computation requires a quadratic number of distance calculations, which is clearly unfeasible for massive datasets. Surprisingly,…
Parallelograms are one of the basic building blocks in two-dimensional tiling. They have important applications in a wide variety of science and engineering fields, such as wireless communication networks, urban transportation, operations…
We study the shrinking Pearson random walk in two dimensions and greater, in which the direction of the Nth is random and its length equals lambda^{N-1}, with lambda<1. As lambda increases past a critical value lambda_c, the endpoint…
Consider~\(n\) nodes~\(\{X_i\}_{1 \leq i \leq n}\) independently distributed in the unit square~\(S,\) each according to a distribution~\(f.\) Nodes~\(X_i\) and~\(X_j\) are joined by an edge if the Euclidean distance~\(d(X_i,X_j)\) is less…
The problem of comparing trees representing the evolutionary histories of cancerous tumors has turned out to be crucial, since there is a variety of different methods which typically infer multiple possible trees. A departure from the…
Random walks on regular bounded degree expander graphs have numerous applications. A key property of these walks is that they converge rapidly to the uniform distribution on the vertices. The recent study of expansion of high dimensional…
Large tree structures are ubiquitous and real-world relational datasets often have information associated with nodes (e.g., labels or other attributes) and edges (e.g., weights or distances) that need to be communicated to the viewers. Yet,…
We study the distribution of sizes of erased loops for loop-erased random walks on regular and fractal lattices. We show that for arbitrary graphs the probability $P(l)$ of generating a loop of perimeter $l$ is expressible in terms of the…
This study is dedicated to precise distributional analyses of the height of non-plane unlabelled binary trees ("Otter trees"), when trees of a given size are taken with equal likelihood. The height of a rooted tree of size $n$ is proved to…
When we represent a network of sensors in Euclidean space by a graph, there are two distances between any two nodes that we may consider. One of them is the Euclidean distance. The other is the distance between the two nodes in the graph,…