Maplesoft Blogger Profile: John May

In a series of posts now imported to the Maplesoft blog (starting here), I have been talking about pseudo-random number sequences, but since part of what kicked off this series was a paper on true random number generation (with LASERS!) I thought I would share some routines I wrote that alllow you to use the two main true random number sources available on the web (neither using lasers, sadly).

In this post I'll introduce is a nice visual test of randomness from signal processing. The main idea of this test to look at how a random sequence correlates with itself.

It's been a while since I wrote one of these random posts, but I still have a couple more I wanted to write.  In this post, I want to describe one of the tests used in the paper that initially inspired this series of posts: the Wald-Wolfowitz runs test.  This test is interesting in that it does not test for uniformity

As alluded to in my previous post in this series, one of the most straight forward ways to test if a PRNG is generating good random sequences is by examining the frequency of 0's and 1's.  This is just a couple lines in Maple using Statistics:

(**) r1 := rand(0..1):L := [seq(r1(), i=1..10000)]:
(**) n := nops(L); tally := `+`(op(L));
(**) Statistics:-ChiSquareGoodnessOfFitTest(
      [n-tally, tally], [n/2, n/2], ':-output'=':-hypothesis');

Today is my birthday, and in fact it is also the birthday of at least one other Maplesoft employee (not surprising since more than 23 people work here - considering the generalized birthday problem, I even know of 3 people here who share the same birthday).  Of course, it turns out that birthdays are not evenly distributed through out the year and so I wanted to know if someone with an August birthday is more likely to share than someone with an April birthday. 

Continuing on in this series of posts, here is a way to test the randomness of a sequence of bits from a PRNG that is the appropriate to the first morning back after the August long weekend.  It is a very fast, and not very formal test done by checking how well a sequence compresses. This is really easy in Maple 14, with the new commands ?StringTools:-Compress and StringTools:-Uncompress which use ...

A while back, someone asked me for a good way to plot a Klein Bottle in Maple. I didn't have a good answer at the time, but I recently stumbled upon the following, which does a pretty good job if you don't mind the use of Heaviside in the parameterization.

plot3d(
   [4*(1-1/2*cos(u))*sin(v),
    6*cos(u)*(1+sin(u))+4*(1-1/2*cos(u))*(cos(u)*(1-Heaviside(u-Pi))+Heaviside(u-Pi))*cos(v+Pi*Heaviside(u-Pi)),

In a previous post, I promised to write about testing the quality of pseudo-random number sequences.  I'll post later about some of the statistical tests often used, but I first wanted to mention a sort of practical test one can do. One of the many things you might want to do with pseudorandomly generated numbers is Monte Carlo integration/simulatation/etc.  As mentioned by acer in this comment, Monte Carlo integration can be shown to work better with some of the pseudorandom number generators (PRNGs) which are considered inferior in a statistical sense.  In this post, we will play with a simple Monte Carlo approximation of π.

A long while ago, I wrote a couple posts (part1 and part2) about mining data from the US SSA website.  I subsequently adapted the code from those blog posts into a visual application with sliders and interactive plots.  If you have played with the new ?MapleCloud functionality in Maple 14, you may have seen it posted already.