Dirk Kroese | The University of Queensland, Australia (original) (raw)
Uploads
Papers by Dirk Kroese
Winter Simulation Conference, 2011
In some rare-event settings, exponentially twisted distributions perform very badly. One solution... more In some rare-event settings, exponentially twisted distributions perform very badly. One solution to this problem is to use mixture distributions. However, it is difficult to select a good mixture distribution for importance sampling. We here introduce a simple adaptive method for choosing good mixture importance sampling distributions.
ABSTRACT We carry out Monte Carlo experiments to study the scaling behavior of shortest path leng... more ABSTRACT We carry out Monte Carlo experiments to study the scaling behavior of shortest path lengths in continuum percolation. These studies suggest that the critical exponent governing this scaling is the same for both continuum and lattice percolation. We use splitting, a technique that has not yet been fully exploited in the physics literature, to increase the speed of our simulations. This technique can also be applied to other models where clusters are grown sequentially.
ABSTRACT A general framework is proposed for the study of the charge transport properties of mate... more ABSTRACT A general framework is proposed for the study of the charge transport properties of materials via Random Walks in Random Environments (RWRE). The material of interest is modelled by a random environment and the charge carrier is modelled by a random walker. The framework combines a model for the fast generation of random environments that realistically mimic materials morphology with an algorithm for efficient estimation of key properties of the resulting random walk. The model of the environment makes use of tools from spatial statistics and the theory of random geometric graphs. More precisely, the disordered medium is represented by a random spatial graph with directed edge weights, where the edge weights represent the transition rates of a Markov Jump Process (MJP) modelling the motion of the random walker. This MJP is a multiscale stochastic process. In the long term, it explores all vertices of the random graph model. In the short term, however, it becomes trapped in small subsets of the state space and makes many transitions in these small regions. This behaviour makes efficient estimation of velocity by Monte Carlo simulations a challenging task. Therefore, we use Aggregate Monte Carlo (AMC), introduced in [5], for estimating the velocity of a random walker as it passes through a realisation of the random environment. In this paper, we prove the strong consistency of the AMC velocity estimator and use this result to conduct a detailed case study, in which we describe the motion of holes in an amorphous mesophase of an organic semiconductor, dicyanovinyl-substituted oligothiophene (DCV4T). In particular, we analyse the effect of system size (i.e. number of molecules) on the velocity of single charge carriers.
Journal of Graph Algorithms and Applications, 2007
The problem of counting the number of s-t paths in a graph is #P-complete. We provide an algorith... more The problem of counting the number of s-t paths in a graph is #P-complete. We provide an algorithm to estimate the solution stochastically, using sequential im- portance sampling. We show that the method works eectiv ely for both graphs and digraphs. We also use the method to investigate the expected number of s-t paths in a random graph of size
Winter Simulation Conference, 2011
In some rare-event settings, exponentially twisted distributions perform very badly. One solution... more In some rare-event settings, exponentially twisted distributions perform very badly. One solution to this problem is to use mixture distributions. However, it is difficult to select a good mixture distribution for importance sampling. We here introduce a simple adaptive method for choosing good mixture importance sampling distributions.
ABSTRACT We carry out Monte Carlo experiments to study the scaling behavior of shortest path leng... more ABSTRACT We carry out Monte Carlo experiments to study the scaling behavior of shortest path lengths in continuum percolation. These studies suggest that the critical exponent governing this scaling is the same for both continuum and lattice percolation. We use splitting, a technique that has not yet been fully exploited in the physics literature, to increase the speed of our simulations. This technique can also be applied to other models where clusters are grown sequentially.
ABSTRACT A general framework is proposed for the study of the charge transport properties of mate... more ABSTRACT A general framework is proposed for the study of the charge transport properties of materials via Random Walks in Random Environments (RWRE). The material of interest is modelled by a random environment and the charge carrier is modelled by a random walker. The framework combines a model for the fast generation of random environments that realistically mimic materials morphology with an algorithm for efficient estimation of key properties of the resulting random walk. The model of the environment makes use of tools from spatial statistics and the theory of random geometric graphs. More precisely, the disordered medium is represented by a random spatial graph with directed edge weights, where the edge weights represent the transition rates of a Markov Jump Process (MJP) modelling the motion of the random walker. This MJP is a multiscale stochastic process. In the long term, it explores all vertices of the random graph model. In the short term, however, it becomes trapped in small subsets of the state space and makes many transitions in these small regions. This behaviour makes efficient estimation of velocity by Monte Carlo simulations a challenging task. Therefore, we use Aggregate Monte Carlo (AMC), introduced in [5], for estimating the velocity of a random walker as it passes through a realisation of the random environment. In this paper, we prove the strong consistency of the AMC velocity estimator and use this result to conduct a detailed case study, in which we describe the motion of holes in an amorphous mesophase of an organic semiconductor, dicyanovinyl-substituted oligothiophene (DCV4T). In particular, we analyse the effect of system size (i.e. number of molecules) on the velocity of single charge carriers.
Journal of Graph Algorithms and Applications, 2007
The problem of counting the number of s-t paths in a graph is #P-complete. We provide an algorith... more The problem of counting the number of s-t paths in a graph is #P-complete. We provide an algorithm to estimate the solution stochastically, using sequential im- portance sampling. We show that the method works eectiv ely for both graphs and digraphs. We also use the method to investigate the expected number of s-t paths in a random graph of size