Random Network Models With Applications in Biology

Central limit theorems in the configuration model

AD Barbour, A Röllin

2019-04-01

We prove a general normal approximation theorem for local graph statistics in the configuration model, together with an explicit b..

When do wireless network signals appear Poisson?

HP Keeler, N Ross, A Xia

2018-08-01

We consider the point process of signal strengths from transmitters in a wireless network observed from a fixed position under mod..

Multivariate approximation in total variation, I: Equilibrium distributions of Markov jump processes

AD Barbour, MJ Luczak, A Xia

2018-05-01

For integer valued random variables, the translated Poisson distributions form a flexible family for approximation in total variat..

Multivariate approximation in total variation, II: Discrete normal approximation

AD Barbour, MJ Luczak, A Xia

2018-05-01

The paper applies the theory developed in Part I to the discrete normal approximation in total variation of random vectors in Z<su..

DYNAMICS of AN INSERTION SEQUENCE INFECTION in A SPATIALLY STRUCTURED ENVIRONMENT

M Bichsel, AD Barbour, A Wagner

2018-03-01

Bacterial insertion sequences (ISs), the simplest form of autonomous mobile DNA, depend on their prokaryote hosts to spread in a s..

A central limit theorem for the gossip process

AD Barbour, Adrian Rollin

2018-01-01

The Aldous gossip process represents the dissemination of information in geographical space as a process of locally deterministic ..

General random walk in a random environment defined on Galton-Watson trees

AD Barbour, A Collevecchio

2017-11-01

We consider a particle performing a random walk on a Galton-Watson tree, when the probabilities of jumping from a vertex to any on..

Stronger Wireless Signals Appear More Poisson

P Keeler, N Ross, A Xia, B Blaszczyszyn

2016-12-01

Keeler et al. recently derived approximation and convergence results, which imply that the point process formed from the signal st..

On explicit form of the stationary distributions for a class of bounded markov chains

S McKinlay, K Borovkov

2016-03-01

We consider a class of discrete-time Markov chains with state space [0, 1] and the following dynamics. At each time step, first th..

Escape from the boundary in Markov population processes

AD Barbour, K Hamza, H Kaspi, FC Klebaner

2015-12-01

Density dependent Markov population processes in large populations of size N were shown by Kurtz (1970), (1971) to be well approxi..

Individual and patch behaviour in structured metapopulation models

AD Barbour, MJ Luczak

2015-09-14

Density dependent Markov population processes with countably many types can often be well approximated over finite time intervals ..

Stein factors for negative binomial approximation in Wasserstein distance

AD Barbour, HL Gan, A Xia

2015-05-01

The paper gives the bounds on the solutions to a Stein equation for the negative binomial distribution that are needed for approxi..

Connecting deterministic and stochastic metapopulation models

AD Barbour, R McVinish, PK Pollett

2015-03-04

In this paper, we study the relationship between certain stochastic and deterministic versions of Hanski’s incidence function mode..

Couplings for locally branching epidemic processes

AD Barbour

2014-12-01

The asymptotic behaviour of many locally branching epidemic models can, at least to first order, be deduced from the limit theory ..

On stationary distributions of stochastic neural networks

K Borovkov, G Decrouez, M Gilson

2014-09-01

The paper deals with nonlinear Poisson neuron network models with bounded memory dynamics, which can include both Hebbian learning..

On the asymptotic behavior of a dynamic version of the neyman contagious point process

K Borovkov

2014-07-03

We consider a dynamic version of the Neyman contagious point process that can be used for modeling the spacial dynamics of biologi..

Mod-discrete expansions

AD Barbour, E Kowalski, A Nikeghbali

2014-04-01

In this paper, we consider approximating expansions for the distribution of integer valued random variables, in circumstances in w..

Asymptotic behaviour of gossip processes and small-world networks

AD Barbour, G Reinert

2013-12-01

Both small-world models of random networks with occasional long-range connections and gossip processes with occasional long-range ..

Approximating the epidemic curve

AD Barbour, G Reinerty

2013-05-28

Many models of epidemic spread have a common qualitative structure. The numbers of infected individuals during the initial stages ..

High host density favors greater virulence: A model of parasite-host dynamics based on multi-type branching processes

K Borovkov, R Day, T Rice

2013-05-01

We use a multitype continuous time Markov branching process model to describe the dynamics of the spread of parasites of two types..

Total variation approximation for quasi-equilibrium distributions, II

AD Barbour, PK Pollett

2012-11-01

Quasi-stationary distributions have been used in biology to describe the steady state behaviour of Markovian population models whi..

Central limit approximations for Markov population processes with countably many types

AD Barbour, MJ Luczak

2012-10-26

When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals..