Related papers: Disassortativity of random critical branching tree…

In this paper we present a new way to understand the timing of branching events in phylogenetic trees. Our method explicitly considers the relative timing of diversification events between sister clades; as such it is complimentary to…

We present a construction of a L\'evy continuum random tree (CRT) associated with a super-critical continuous state branching process using the so-called exploration process and a Girsanov's theorem. We also extend the pruning procedure to…

Population-size dependent branching processes (PSDBP) and controlled branching processes (CBP) are two classes of branching processes widely used to model biological populations that exhibit logistic growth. In this paper we develop…

Although there is increasing evidence of criticality in the brain, the processes that guide neuronal networks to reach or maintain criticality remain unclear. The present research examines the role of neuronal gain plasticity in time-series…

Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…

A compacted binary tree is a graph created from a binary tree such that repeatedly occurring subtrees in the original tree are represented by pointers to existing ones, and hence every subtree is unique. Such representations form a special…

We consider random recursive trees that are grown via community modulated schemes that involve random attachment or degree based attachment. The aim of this paper is to derive general techniques based on continuous time embedding to study…

In several real-world networks like the Internet, WWW etc., the number of links grow in time in a non-linear fashion. We consider growing networks in which the number of outgoing links is a non-linear function of time but new links between…

Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism…

Real-world networks process structured connections since they have non-trivial vertex degree correlation and clustering. Here we propose a toy model of structure formation in real-world weighted network. In our model, a network evolves by…

Problem definition. In retailing, discrete choice models (DCMs) are commonly used to capture the choice behavior of customers when offered an assortment of products. When estimating DCMs using transaction data, flexible models (such as…

We propose a generalized model for uniform recursive tree (URT) by introducing an imperfect growth process, which may generate disconnected components (clusters). The model undergoes an interesting phase transition from a singly connected…

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…

In distributed applications, such as energy demand forecasting at the substation level or federated learning, a large number of related tasks must be learned by different models, while the exact task relationships are unknown. We propose…

The structure of complex networks in previous research has been widely described as scale-free networks generated by the preferential attachment model. However, the preferential attachment model does not take into account the detailed…

Stochastic branching processes are a classical model for describing random trees, which have applications in numerous fields including biology, physics, and natural language processing. In particular, they have recently been proposed to…

The minimum spanning tree (MST) is a combinatorial optimization problem: given a connected graph with a real weight ("cost") on each edge, find the spanning tree that minimizes the sum of the total cost of the occupied edges. We consider…

The Bayesian Context Trees (BCT) framework is a recently introduced, general collection of statistical and algorithmic tools for modelling, analysis and inference with discrete-valued time series. The foundation of this development is built…

We show that a randomly perturbed digraph, where we start with a dense digraph $D_\alpha$ and add a small number of random edges to it, will typically contain a fixed orientation of a bounded degree spanning tree. This answers a question…

Construction of phylogenetic trees and networks for extant species from their characters represents one of the key problems in phylogenomics. While solution to this problem is not always uniquely defined and there exist multiple methods for…