Monday, November 1, 2010

Day 13

Today I mostly did teaching related stuff due to the fact that my DEs class had their exam this morning and the PDEs class has theirs on wednesday. So lots of students visiting to ask questions. Plus I had to write the exam and solutions!

This evening though I read a paper I downloaded from a recent issue of Mathematical and Computer Modelling. Patanarapeelert et al reported on as study they carried out where they took the data generated by CA models of tumor growth ( like the ones I do ) and applied some technique to it to determine the coefficient functions for a stochastic de model of the form
dX_t = h dt + g dW.
Thereby allowing for a macroscopic model to be derived from a microscopic model.

I think I get the majority of it, but it's not all clear for me unfortunately. Plus the language was a bit scrappy but that's ok.

The problem is I'm not exactly sure I get the point of what they did. They very briefly skim over what I consider to be the most important bit in the last sentence or so. That being that they could use microscopic understanding to build a CA model, generate in silica data, build the macroscopic model and then use it to make recommendations or conclusions at the macroscopic level (eg x will happen to the tumor due to y being applied to the immune system).

Anyway I think i will ask dr Simpson if it's worth looking into it any further... Or if we (he) can do something better to the same end.

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