This is a follow-up to yesterday’s post. In that post we looked at iterates of the function f(x) = exp(…
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Allow Simple Cluster Creation with Full Admin Control Using Cluster Policies
What is a Databricks cluster policy? A Databricks cluster policy is a template that restricts the way users interact with…
Continue ReadingVariation on cosine fixed point
If you enter any number into a calculator and repeatedly press the cosine key, you’ll eventually get 0. 73908513, assuming…
Continue ReadingLogistic bifurcation diagram in detail
The image below if famous. I’ve seen it many times, but rarely with a detailed explanation. If you’ve ever seen…
Continue ReadingFixed points of the Cliff random number generator
I ran across the Cliff random number generator yesterday. Given a starting value x0 in the open interval (0, 1),…
Continue ReadingKepler and the contraction mapping theorem
We’ll make this statement more precise and give a historically important application.Definitions and theoremA function f on a metric space…
Continue ReadingUsing fixed and random effects models for panel data in Python
Specifically, researchers often must decide whether to use a fixed or random effects approach in an analysis like this.In this…
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