Related papers: From trees to graphs: collapsing continuous-time b…
We obtain local weak limits in probability for Collapsed Branching Processes (CBP), which are directed random networks obtained by collapsing random-sized families of individuals in a general continuous-time branching process. The local…
Multitype branching processes (MTBP) model branching structures, where the nodes of the resulting tree are objects of different types. One field of application of such models in biology is in studies of cell proliferation. A sampling scheme…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…
Continuous time Bayesian networks (CTBNs) describe structured stochastic processes with finitely many states that evolve over continuous time. A CTBN is a directed (possibly cyclic) dependency graph over a set of variables, each of which…
Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more…
Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…
A controlled branching process (CBP) is a modification of the standard Bienaym\'e-Galton-Watson process in which the number of progenitors in each generation is determined by a random mechanism. We consider a CBP starting from a random…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
Real-world networks tend to be scale free, having heavy-tailed degree distributions with more hubs than predicted by classical random graph generation methods. Preferential attachment and growth are the most commonly accepted mechanisms…
Concept Bottleneck Models (CBMs) provide explicit interpretations for deep neural networks through concepts and allow intervention with concepts to adjust final predictions. Existing CBMs assume concepts are conditionally independent given…
In the critical beta-splitting model of a random $n$-leaf rooted tree, clades are recursively (from the root) split into sub-clades, and a clade of $m$ leaves is split into sub-clades containing $i$ and $m-i$ leaves with probabilities…
Branching processes form an important family of stochastic processes that have been successfully applied in many fields. In this paper, we focus our attention on controlled multi-type branching processes (CMBPs). A Feller-type diffusion…
We are interested in the analysis of very large continuous-time Markov chains (CTMCs) with many distinct rates. Such models arise naturally in the context of reliability analysis, e.g., of computer network performability analysis, of power…
Dynamical processes on complex networks such as information propagation, innovation diffusion, cascading failures or epidemic spreading are highly affected by their underlying topologies as characterized by, for instance, degree-degree…
Given a finite sequence of graphs, e.g., coming from technological, biological, and social networks, the paper proposes a methodology to identify possible changes in stationarity in the stochastic process generating the graphs. In order to…
Our purpose is to estimate the posterior distribution of the parameters of interest for controlled branching processes (CBPs) without prior knowledge of the maximum number of offspring that an individual can give birth to and without…
Continuous-time Bayesian networks (CTBNs) are graphical representations of multi-component continuous-time Markov processes as directed graphs. The edges in the network represent direct influences among components. The joint rate matrix of…
We introduce Graph Neural Processes (GNP), inspired by the recent work in conditional and latent neural processes. A Graph Neural Process is defined as a Conditional Neural Process that operates on arbitrary graph data. It takes features of…
We introduce a process where a connected rooted multigraph evolves by splitting events on its vertices, occurring randomly in continuous time. When a vertex splits, its incoming edges are randomly assigned between its offspring and a…
Tanglegrams are a special class of graphs appearing in applications concerning cospeciation and coevolution in biology and computer science. They are formed by identifying the leaves of two rooted binary trees. We give an explicit formula…