- Your exam revisions are due today.
- Also due today: your data entry. Please submit
your data to me electronically, so that we can
start a group database of the Fletcher data.
Submit one file.
- Please revise your Keeling reports (due next Friday). I
want to feature one
report to give you an idea of some things that
I'd like you to shoot for....
Please also include confidence intervals for amplitude $A$ and phase $t_0$.
I'll grade based more on the final paper than on the original.
- Last time we began discussing non-linear regression, with a discussion of
Newton's method. It's got Newton's name on it, so it's got to be good!
The key to non-linear regression is linear regression! That may seem odd, but I will mention again that frequently in mathematics we often cast a problem from the non-linear world over to where we obtain a linear problem, then bring that solution back (and hope for the best).
In the case of the linearizations we have done, we only did this once. In the case of non-linear regression, we will do it multiple times (iteratively), hoping for constant improvement.
-
The data is the number of bodies in rigor mortis from two hours on: {2, 14, 31, 14, 20, 11, 7, 4, 7, 1, 1, 2}.
-
As we think about modeling the onset of rigor mortis, we
might start with the Bestiary of
functions, from Ben Bolker's Ecological Models and
Data in R. Do we hear any songs that sound like our data?
If not, we may have to go off-road, to mix metaphors....
-
In the course of that modeling exercise you'll see that we can
perform non-linear regression by iteratively solving linear
problems, to approximate a solution to the non-linear
problem.
I'll try to show how this is a generalization of Newton's method.
- PostmortemChanges.pdf (source) -- includes the rigor mortis data, and a description of the process.
- The history of fracking.
- Study: Fracking prompts global spike in atmospheric methane: "If we can stop pouring methane into the atmosphere, it will dissipate", he said. "It goes away pretty quickly, compared to carbon dioxide. It's the low-hanging fruit to slow global warming."
- The Fracking Industry's Methane Problem Is a Climate Problem (shows some of the methane leak impacts of fracking).
- Robert W. Howarth lecture (12/14/2019) on methane, fracking, and climate change: "Professor of Ecology & Environmental Biology at Cornell University, asking "Is Shale Gas a Major Driver of Recent Increases in Global Atmospheric Methane?" Howarth, who participated in the 2015 Paris Climate Agreement, among other things, is a world authority on the effects of human activity on the environment." He addresses the question of the shape of the methane curve at 1 hour, 5 minutes or so.
- "The
IPCC stands by its equation of 450 ppm = 2 degrees C [of
warming]....": For years scientists have said that if
atmospheric levels of carbon dioxide reach 450 parts per million (ppm)
the planet would heat up by an average of 2 degrees Celsius above
pre-industrial levels. They have also said that if the world crosses
that threshold, ecosystems worldwide would suffer serious damage.
[ael: by the way -- ecosystems worldwide are already suffering serious damage.... The world won't "suddenly heat up" if we reach 450 ppm -- it's heating up right now, and we're seeing bumblebees struggle with the heat, for example. They pollinate our food -- think about it....]