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2004

Kouritzin, Michael, Long, H., Sun, W.

Herein, we consider direct Markov chain approximations to the Duncan–Mortensen–Zakai equations for nonlinear filtering problems on regular, bounded domains. For clarity of presentation, we restrict our attention to reflecting diffusion signals with symmetrizable generators. Our Markov chains are...

2002-01-01

Hans F. Weinberger, Mark A. Lewis, Bingtuan Li

The discrete-time recursion system \un+1=Q[\un] with \un(x) a vector of population distributions of species and Q an operator which models the growth, interaction, and migration of the species is considered. Previously known results are extended so that one can treat the local invasion of an...

2002-01-01

Lewis, Mark A., Bingtuan Li, Hans F. Weinberger

 One crucial measure of a species' invasiveness is the rate at which it spreads into a competitor's environment. A heuristic spread rate formula for a spatially explicit, two-species competition model relies on `linear determinacy' which equates spread rate in the full nonlinear model with spread...

2002-01-01

MacIsaac, H.J., Lewis, Mark A., Robbins, T.C.

The spread of nonindigenous species in aquatic ecosystems provides an opportunity to develop new perspectives on the invasion process. In this paper we review existing invasion models, most of which were developed to describe invasions of terrestrial habitats, and propose an alternative that...

2002

Kouritzin, Michael, Long, H.

In the context of simulating the transport of a chemical or bacterial contaminant through a moving sheet of water, we extend a well-established method of approximating reaction-diffusion equations with Markov chains by allowing convection, certain Poisson measure driving sources and a larger...

2001-01-01

Lewis, Mark A., Owen, Markus R.

High-frequency ventilation isa radical departure from conventional lung ventilation, with frequenciesgreater than 2Hz, and volumesp er breath much smaller than the anatomical deadspace. Its use has been shown to benefit premature infants and patients with severe respiratory distress, but a vital...

2001-01-01

M. R. OWEN, M. A. LEWIS

Observations on Mount St Helens indicate that the spread of recolonizing lupin plants has been slowed due to the presence of insect herbivores and it is possible that the spread of lupins could be reversed in the future by intense insect herbivory [Fagan, W. F. and J. Bishop (2000). Trophic...

2001-01-01

Holt, R. D., Lewis, Mark A., Keitt, T. H.

All species’ ranges are the result of successful past invasions. Thus, models of species’ invasions and their failure can provide insight into the formation of a species’ geographic range. Here, we study the properties of invasion models when a species cannot persist below a critical population...

2001-01-01

Clark, James S., Lewis, Mark A., Horvath, Lajos

For populations having dispersal described by fat‐tailed kernels (kernels with tails that are not exponentially bounded), asymptotic population spread rates cannot be estimated by traditional models because these models predict continually accelerating (asymptotically infinite) invasion. The...

1997

Kouritzin, Michael

Herein, an averaging theory for the solutions to Cauchy initial value problems of arbitrary order,ε-dependent parabolic partial differential equations is developed. Indeed, by directly developing bounds between the derivatives of the fundamental solution to such an equation and derivatives of the...