Related papers: Generalized Nonlinear Yule Models
We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new…
A network evolution with predicted tail and extremal indices of PageRank and the Max-Linear Model used as node influence indices in random graphs is considered. The tail index shows a heaviness of the distribution tail. The extremal index…
In this paper, we propose an evolving network model growing fast in units of module, based on the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected…
We propose a model of a growing network, in which preferential linking is combined with partial inheritance of connectivity (number of incoming links) of individual nodes by new ones. The nontrivial version of this model is solved exactly…
We study a nonlinear recombination model from population genetics as a combinatorial version of the Kac-Boltzmann equation from kinetic theory. Following Kac's approach, the nonlinear model is approximated by a mean field linear evolution…
Stochastic modelling of fatigue (and other material's deterioration), as well as of cumulative damage in risk theory, are often based on compound sums of independent random variables, where the number of addends is represented by an…
Most classification methods are based on the assumption that data conforms to a stationary distribution. The machine learning domain currently suffers from a lack of classification techniques that are able to detect the occurrence of a…
To understand the growing phenomena of new vocabulary on nationwide online social media, we analyzed monthly word count time series extracted from approximately 1 billion Japanese blog articles from 2007 to 2019. In particular, we first…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
A model describing the dynamics related to the spreading of non-lethal infectious diseases in a fixed-size population is proposed. The model consists of a non-linear delay-differential equation describing the time evolution of the increment…
Collections of journal papers, often referred to as 'citation networks', can be modeled as a collection of coupled bipartite networks which tend to exhibit linear growth and preferential attachment as papers are added to the collection.…
We consider a stochastic process for the generation of species which combines a Yule process with a simple model for hybridization between pairs of co-existent species. We assume that the origin of the process, when there was one species,…
Fertility plans, measured by the number of planned children, have been found to be affected by education and family background via complex tail dependencies. This challenge was previously met with the use of non-parametric jittering…
In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the…
In this article, we provide different representations for a time-fractional birth and death process $N_{\alpha}(t)$, whose transition probabilities are governed by a time-fractional system of differential equations. More specifically, we…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…
Yule's 1925 paper introducing the branching model that bears his name was a landmark contribution to the biodiversity sciences. In his paper, Yule developed stochastic models to explain the observed distribution of species across genera and…
A subdiffusion problem in which the diffusion term is related to a stable stochastic process is introduced. Linear models of these systems have been studied in a general way, but non-linear models require a more specific analysis. The model…
We present a theory for the growth dynamics of the World Wide Web that takes into account the wide range of stochastic growth rates in the number of pages per site, as well as the fact that new sites are created at different times. This…
There are a few different ways to extend regular nonlinear dynamical systems by introducing power-law memory or considering fractional differential/difference equations instead of integer ones. This extension allows the introduction of…