Related papers: Uniform attachment with freezing
We prove almost sure convergence of the maximum degree in an evolving tree model combining local choice and preferential attachment. At each step in the growth of the graph, a new vertex is introduced. A fixed, finite number of possible…
We show, under natural conditions, that uniform rooted trees with fixed degree sequence converge after renormalization toward inhomogeneous continuum random trees (ICRT). We also provide a sharp upper-bound for the tail of their heights. We…
We consider the dynamics of a population spatially structured in colonies that are vulnerable to catastrophic events occurring at random times, which randomly reduce their population size and compel survivors to disperse to neighboring…
Random Forest is an ensemble of decision trees based on the bagging and random subspace concepts. As suggested by Breiman, the strength of unstable learners and the diversity among them are the ensemble models' core strength. In this paper,…
Tree ensembles are flexible predictive models that can capture relevant variables and to some extent their interactions in a compact and interpretable manner. Most algorithms for obtaining tree ensembles are based on versions of boosting or…
We consider linear preferential attachment random trees with additive fitness, where fitness is defined as the random initial vertex attractiveness. We show that when the fitness distribution has positive bounded support, the weak local…
We present a new, physically-intuitive model of ice-lens formation and growth during the freezing of soils and other dense, particulate suspensions. Motivated by experimental evidence, we consider the growth of an ice-filled crack in a…
We consider a procedure to reduce simply generated trees by iteratively removing all leaves. In the context of this reduction, we study the number of vertices that are deleted after applying this procedure a fixed number of times by using…
We work with attracting subshifts generated by substitutions which are also irreducible parageometric automorphisms of free groups. For such a dynamical system, we construct a tree substitution to approximate the repelling real tree of the…
A Yule tree is the result of a branching process with constant birth and death rates. Such a process serves as an instructive null model of many empirical systems, for instance, the evolution of species leading to a phylogenetic tree.…
Fixed effects models are very flexible because they do not make assumptions on the distribution of effects and can also be used if the heterogeneity component is correlated with explanatory variables. A disadvantage is the large number of…
We consider a model of random tree growth, where at each time unit a new vertex is added and attached to an already existing vertex chosen at random. The probability with which a vertex with degree $k$ is chosen is proportional to $w(k)$,…
A fringe subtree of a rooted tree is a subtree induced by one of the vertices and all its descendants. We consider the problem of estimating the number of distinct fringe subtrees in two types of random trees: simply generated trees and…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…
The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…
The main substance of the paper concerns the growth rate and the classification (ergodicity, transience) of a family of random trees. In the basic model, new edges appear according to a Poisson process of parameter $\lambda$ and leaves can…
We obtained Pearson's coefficient of strongly correlated recursive networks growing by preferential attachment of every new vertex by $m$ edges. We found that the Pearson coefficient is exactly zero in the infinite network limit for the…
A random walk on a regular tree (or any non-amenable graph) has positive speed. We ask whether such a walk can be slowed down by applying carefully chosen time-dependent permutations of the vertices. We prove that on trees the random walk…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…