[FRIAM] FW: Mathematical Inquiry

[Pieter Steenekamp]

My approach would be as follows:
a) Start with MS Excel. It is very simple to use and help is very widely
available. One can very easily draw very nice curves and dependent on what
intuition comes out of observing the curves fit different simple models to
the data and again draw curves of the model outputs against the original
curves.
b) If this does not give satisfactory results, I would use H2O in R to
build a deep learning model based on the data. There are very powerful data
visualization packages in R to really go overboard to display the data in
very fancy ways and then the deep learning models can very easily
incorporate many more variables and more sophisticated models.

On Mon, 26 Aug 2019 at 11:42, Nick Thompson <nickthompson at earthlink.net>
wrote:

>
>
> Dear Mathematical Friammers,
>
>
>
> What follows is a problem in mathematics, which, of course, has nothing to
> do with me.
>
>
>
> *Jones is a diabetic, and he has a glucose monitor that gives him his
> exact blood glucose level moment to moment.  Jones notices at that after
> breakfast, his blood sugars behave in in very different manners, even
> though he eats exactly the same food every day, doesn’t exercise at that
> time of day ever, and takes exactly the same amount of insulin.  Some
> mornings, his blood sugar rises steadily for several hours after a meal,
> sometimes it falls steadily.  Only rarely does it remain steady.  One
> variable seems left for Jones to control and that is the exact timing of
> the relation between when he take his insulin and the time he begins his
> meal.  *
>
>
>
> *So, Jones imagines a model as follows.  Because Jones always takes
> exactly the amount of insulin necessary to account for the amount of sugar
> he eats, he assumes that the curves of insulin activity and sugar activity
> are both normal curves, with the same median time and the same sd and,
> therefore, the same area under the curve.  However, one curve is offset
> from the other because sometimes Jones takes his insulin before he eats his
> sugar and sometimes he eats his sugar before he takes his insulin.  Bearing
> in mind that the Insulin curve SUBTRACTS from the sugar curve, Jones
> wonders about the shape of the difference curve that results from different
> offsets between eating his meal and taking his insulin.  He wonders if,
> perhaps, that this whole dramatic failure of control, could be due to the
> fact that on some days he takes his insulin a little too early and the
> sugar in the meal is slow to catch up and on other days, he takes it too
> late and the insulin is slow to  catch up.  Thus, the correct offset is a
> tipping point, an unstable equilibrium which is very difficult to achieve.
> *
>
>
>
> *Jones is not a mathematician, but he hangs around with mathematicians,
> and he suspects that there is a software that is readily available on line
> for free that would allow him to display the different curves that result
> from the different offsets and, perhaps, even better, display the function
> that relates the integral of the difference function as a function of the
> offset.   This function might have some interesting properties that could
> be used to guide Jones’s injection behavior.  *
>
>
>
> Does anybody have any thoughts on Jones’s predicament?
>
>
>
> Not that I care, but still,
>
>
>
> Nick
>
>
>
> Nicholas S. Thompson
>
> Emeritus Professor of Psychology and Biology
>
> Clark University
>
> http://home.earthlink.net/~nickthompson/naturaldesigns/
>
>
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