Abstract This note extends the work of Foss and Tweedie (1998), who showed that availability of the classic Propp and Wilson (1996) Coupling from The Past algorithm is essentially equivalent to uniform ergodicity for a Markov chain (see also Hobert and Robert 2004). In this note we show that all geometrically ergodic chains possess dominated Coupling from The Past algorithms (not necessarily pr...

The complexity of geometric algorithms is often express in terms of the input size and sometimes of the output size, but the behavior of these algorithms may depend drastically on the geometric distribution of the input. The difference between the best-case and the worst-case can be important. An alternative is to analyze these algorithms under the hypothesis of a probabilistic distribution of ...

This paper describes an effective and intuitive method to control deformable objects using geometric constraints. To achieve a natural and plausible interaction with deformable objects and to setup the desirable initial conditions of simulation, users should be able to define and control the geometric constraints intuitively. Users should be able to utilize the simulation as a problem solving p...

The geometrical approach to phase transitions is illustrated by simulating the hightemperature representation of the Ising model on a square lattice.

Specialised modelling and simulation methods implementing simplified physical models are valuable generators of insight. Template-based geometric simulation is a specialised method for modelling flexible framework structures made up of rigid units. We review the background, development and implementation of the method, and its applications to the study of framework materials such as zeolites an...