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| In the first part of the talk, I will discuss an extension of the UCLA crime model to incorporate more realistic locomotion of criminals. Instead of assuming that the criminals follow a biased brownian motion [as in the original model], we ask what happens when they follow a biased Levy flight. It turns out that from the point of view of the criminal, there is an "optimal" Levy flight exponent which maximizes the criminal's chance of committing a burglary.
In the second part of the talk, I will discuss the Keller-Segel model with logistic self-production terms that exhibits complex spatio-temporal dynamics of spikes. Unlike the "classical" KS model, we show that it is possible to stabilize a single interior spike, and we compute analytically a critical threshold which is responsible for spike stabilization. |
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