Related papers: On Sibuya trees and forests
The spread of infectious disease in a human community or the proliferation of fake news on social media can be modeled as a randomly growing tree-shaped graph. The history of the random growth process is often unobserved but contains…
One of the first successes of neutral ecology was to predict realistically-broad distributions of rare and abundant species. However, it has remained an outstanding theoretical challenge to describe how this distribution of abundances…
Gibbs-type priors are widely used as key components in several Bayesian nonparametric models. By virtue of their flexibility and mathematical tractability, they turn out to be predominant priors in species sampling problems, clustering and…
We investigate the profile of random P\'olya trees of size $n$ when only nodes of degree $d$ are counted in each level. It is shown that, as in the case where all nodes contribute to the profile, the suitably normalized profile process…
We study a class of branching processes in which the offspring distribution is not specified directly but is induced by a cycle of internal colony growth, catastrophic reduction and structured dispersal. The parameters governing growth,…
Isolation Forest (iForest) stands out as a widely-used unsupervised anomaly detector, primarily owing to its remarkable runtime efficiency and superior performance in large-scale tasks. Despite its widespread adoption, a theoretical…
In this paper, we investigate certain combinatorial numbers, the \textit{moment generating Stirling numbers}. They are a special case of Hsu's generalized Stirling numbers and satisfy many more properties and combinatorial identities than…
We introduce some new generalized stochastic orderings (in the spirit of relative ageing) which compare probability distributions with the exponential distribution. These orderings are useful to understand the phenomenon of positive ageing…
Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…
We consider the counting problem of the number of \textit{leaf-labeled increasing trees}, where internal nodes may have an arbitrary number of descendants. The set of all such trees is a discrete representation of the genealogies obtained…
We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [Berstel et al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely studied…
We propose Partition Tree, a novel tree-based framework for conditional density estimation over general outcome spaces that supports both continuous and categorical variables within a unified formulation. Our approach models conditional…
We introduce the quasi-ordinarization transform of a numerical semigroup. This transform will allow to organize all the semigroups of a given genus in a forest rooted at all quasi-ordinary semigroups with the given genus. This construction…
For a pair consisting of a gene tree and a species tree, the ancestral configurations at an internal node of the species tree are the distinct sets of gene lineages that can be present at that node. Ancestral configurations appear in…
We introduce regenerative tree growth processes as consistent families of random trees with n labelled leaves, n>=1, with a regenerative property at branch points. This framework includes growth processes for exchangeably labelled Markov…
In invasion percolation, the edges of successively maximal weight (the outlets) divide the invasion cluster into a chain of ponds separated by outlets. On the regular tree, the ponds are shown to grow exponentially, with law of large…
In a geographically distributed population, assortative clustering plays an important role in evolution by modifying local environments. To examine its effects in a linear habitat, we consider a one-dimensional grid of cells, where each…
In this paper we present new results on the enumeration of parking functions and labeled forests. We introduce new statistics on parking functions, which are then extended to labeled forests via bijective correspondences. We determine the…
We consider linear preferential attachment trees, and show that they can be regarded as random split trees in the sense of Devroye (1999), although with infinite potential branching. In particular, this applies to the random recursive tree…
This paper deals into the long-term behavior of subordinated critical branching processes with migration. We focus on scenarios where emigration is the dominant factor and introduce additional randomness in timing through a subordination…