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 Reading## Variation 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 Reading## Logistic 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 Reading## Fixed 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 Reading## Kepler 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 Reading## Using 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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