Finding the right math for medical problems

The linked article is for SIAM News, the magazine for members of the Society for Industrial and Applied Mathematics (SIAM). However, even though the main audience for this magazine is professional mathematicians, I wrote it to be understandable even if you gloss over the math. And it involves the word “tortuosity”, which is just fun to say.

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A Nonparametric Swiss Army Knife for Medicine

For SIAM News:

The complexity of living things is frequently humbling for mathematicians. Even a single cell contains a plethora of processes and complicated interactions that tractable mathematical models cannot easily describe. Researchers have applied nonlinear dynamics, mechanical analogs, and numerous other techniques to understand biological systems, but the tradeoffs of modeling often err on the side of reductionism.

For this reason, Heather Harrington of the University of Oxford and her collaborators are turning to global mathematical methods and drawing on experimental data to identify the best techniques. Harrington described several of these methods during her invited talk at the 2021 SIAM Conference on Applications of Dynamical Systems, which took place virtually earlier this year.

“The way that we look at dynamical systems is usually in a small region of the parameter space,” Harrington said. This approach is helpful if one knows a lot about the model and its parameters, but it can be hard to extract detailed predictions from the model if the parameters in question range over large values. “In biology, we often don’t know if the system is very close to a value in parameter space because the variables or parameters are difficult to measure or the data is too messy,” she added.

[read the rest at SIAM News]

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