Related papers: The total path length of split trees
We study the joint distribution of the number of occurrences of members of a collection of nonoverlapping motifs in digital data. We deal with finite and countably infinite collections. For infinite collections, the setting requires that we…
In the previous chapters, we explored the effects of resetting on networks considering one and two nodes. In this chapter, we will describe a generalization of random walks with resetting to an arbitrary number of nodes $\mathcal{M}$. In…
We focus on the problem of performing random walks efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain a random walk sample. We first present a fast sublinear…
Random forests are a statistical learning method widely used in many areas of scientific research because of its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional…
Phylogenetic networks extend phylogenetic trees to model non-vertical inheritance, by which a lineage inherits material from multiple parents. The computational complexity of estimating phylogenetic networks from genome-wide data with…
Traditional studies of memory for meaningful narratives focus on specific stories and their semantic structures but do not address common quantitative features of recall across different narratives. We introduce a statistical ensemble of…
We explore a generating function trick which allows us to keep track of infinitely many statistics using finitely many variables, by recording their individual distributions rather than their joint distributions. Building on previous work…
During the last decade, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs) have been shown to work well in practice and to possess theoretical guarantees such as probabilistic…
We consider in this paper the problem of discovering, via a traceroute algorithm, the topology of a network, whose graph is spanned by an infinite branching process. A subset of nodes is selected according to some criterion. As a measure of…
It is known that maximal entropy random walks and partition functions that count long paths on graphs tend to become localized near nodes with a high degree. Here, we revisit the simplest toy model of such a localization: a regular tree of…
As a flexible nonparametric learning tool, the random forests algorithm has been widely applied to various real applications with appealing empirical performance, even in the presence of high-dimensional feature space. Unveiling the…
In 1996, Bodlaender showed the celebrated result that an optimal tree decomposition of a graph of bounded treewidth can be found in linear time. The algorithm is based on an algorithm of Bodlaender and Kloks that computes an optimal tree…
The properties of randomly evolving special trees having defined and analyzed already in two earlier papers (arXiv:cond-mat/0205650 and arXiv:cond-mat/0211092) have been investigated in the case when the continuous time parameter converges…
In this paper, we build on recent results by Chauve et al. (2014) and Bahrani and Lumbroso (2017), which combined the split-decomposition, as exposed by Gioan and Paul, with analytic combinatorics, to produce new enumerative results on…
R\'emy's algorithm is a Markov chain that iteratively generates a sequence of random trees in such a way that the $n^{\mathrm{th}}$ tree is uniformly distributed over the set of rooted, planar, binary trees with $2n+1$ vertices. We obtain a…
Motivated by the study of random temporal networks, we introduce a class of random trees that we coin \emph{uniform temporal trees}. A uniform temporal tree is obtained by assigning independent uniform $[0,1]$ labels to the edges of a…
Given any regularly varying dislocation measure, we identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we obtain continuum random tree limits of…
We study the properties of random walks on complex trees. We observe that the absence of loops reflects in physical observables showing large differences with respect to their looped counterparts. First, both the vertex discovery rate and…
This paper is concerned with the reliable inference of optimal tree-approximations to the dependency structure of an unknown distribution generating data. The traditional approach to the problem measures the dependency strength between…
Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper we show that in case the coupled…