Both small-world models of random networks with occasional long-range connections and gossip processes with occasional long-range transmission of information have similar characteristic behaviour. The long-range elements appreciably reduce the effect...

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Quasi-stationary distributions have been used in biology to describe the steady state behaviour of Markovian population models which, while eventually certain to become extinct, nevertheless maintain an apparent stochastic equilibrium for long period...

When approximating the joint distribution of the component counts of a decomposable combinatorial structure that is ‘almost’ in the logarithmic class, but nonetheless has irregular structure, it is useful to be able first to establish that the distri...

When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since there is usually no obvious natural upper limit on the number of individuals in a patch, this leads...

Many models of epidemic spread have a common qualitative structure. The numbers of infected individuals during the initial stages of an epidemic can be well approximated by a branching process, after which the proportion of individuals that are susce...

Quasi–stationary distributions, as discussed by Darroch & Seneta (1965), have been used in biology to describe the steady state behaviour of population models which, while eventually certain to become extinct, nevertheless maintain an apparent stocha...

I highlight two advantages of adopting a 'new trade' approach to trade negotiations. First, it allows for a view of trade negotiations in which producer interests play a prominent role. And second, it lends itself naturally to quantitative analyses o...

The main result is a two-dimensional identity in law. Let (B t ,L t ) and (β t ,λ t ) be two independent pairs of a linear Brownian motion with its local time at 0. Let A t =∫ 0 t exp(2B s )ds. Then, for fixed t, the pair (sinh(B t ),sinh(L t )) has ...

In this expository note, we present a transparent proof of Toponogov's theorem for Alexandrov spaces in the general case, not assuming local compactness of the underlying metric space. More precisely, we show that if M is a complete geodesic metric s...