My main area of interest is mathematical Biology. I got a PhD in 1982 in Applied Mathematics at the Weizmann Institute of Science, Rehovot, Israel, with Prof Lee A. Segel. I am a member of the Mathematics Department and the Institute of Applied Mathematics (IAM) at UBC. I am a former president of the Society for Mathematical Biology.
Below are some problems and areas that I am working in. See also the recent project, Biomedical Models of Cellular and Physiological Systems and Disease funded under the umbrella of MITACS described on another web page.
For some pictures related to the actin work, click
Here.
With Athan Spiros I have been working on simulations of neuroinflammation believed to be associated with Alzheimer's Disease. Our evolving website contains interactive (Java-based) simulations that can be used to study some of the phenomena associated with this type of inflammatory phenomenon.
Aggregation and migration are collective phenomena displayed by a variety of social organisms (insects, fish, fowl) often with important economic implications. I have studied group behaviour of various sorts over the years. Mathematical models for such phenomena are traditionally cast in terms of partial differential equations with terms for interaction and for random motion. However, these models generally fail to produce travelling band solutions, the correct description of a group moving together as a cohesive unit . Currently under investigation with A. Mogilner are individual-based models for swarming behaviour.
For simulations related to attraction-repulsion mechanisms of spacing of individuals in a group, related to our recent work, see this web site.
This research has a basic mathematical modelling perspective.
However, it has implications beyond this, to behavioural ecology (the
behaviour of social units), resource conservation (fish),
management strategies (bees), and pest control (locusts).
For a picture of army ants in a mill, click here.
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