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I have always preferred the notation  for the derivative of

Green Cars...

December 15 2010 Tom 4 724 MapleSim

My father’s first car when our family moved to North America was a 1970 Buick Skylark sedan, and the color was a majestic deep green. I was seven years old at the time and this was my first experience with a green car. It’s ironic that my life in North America started with a green car and has come full circle with green cars all over the place as far as my job is concerned. But of course, today’s green car is really about highly fuel efficient cars...

Like many in the technology industry, I am a big fan of science fiction films and I’ve written in the past about how exciting it is for me to have a job where science fiction and reality literally meet. Over the past few months, several key projects from various Maple and MapleSim users caught my attention for various reasons and once again, I was forced to giggle publicly as the shear cool factor of these applications overcame my normal mature demeanor.

The Canadian Lotto649 draws are randomized the old fashioned way, the draws are held using a Ryo-Catteau Tulipe ball machine made by a well respected French Company. The draws are video recorded in a secure studio, and broadcast live.  There is no reason to suspect that these draws might not be random, but let us look at some ways we might detect it if it were not random.

You could look at the Lottery draws as a generator for a binary sequence as I did in my previous post, but as Robert Israel pointed out in the comments, that encoding can hide some non-random behavior (e.g. if the number 25 appeared in every draw, that encoding would not appear less random).

This is not really the next part in my randomness series, but more of an aside.  I used Maple's embedded components to use the Lotto649 drawing data from my last post to create a historical lottery simulator.  Basically, you fill in your prefered numbers, and it simulates you playing the lottery in every draw since 1982.

In this series of blog posts, I have picked on Baseball win-loss records already.  Looking for other sources of things that might or might not be random, I decided to look at lottery draws.  Since I live in Canada, the obvious lottery to look at is the national Lotto 6/49.

A lotto 6/49 draw consists of drawing 6 numbered balls from...

I lived in the UK before making the barely-considered decision to move to Canada.  I still have savings denominated in pounds sterling (all dutifully declared on my Canadian tax return).  Accordingly, I keep a close watch on the GBP-CAD exchange rate so I have some sense of my net worth.

When I arrived in Canada in July 2008, one pound sterling bought $2, down from $2.30 two years before that.  Today, the pound has devalued further and is worth around...

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).

I spent this past week preparing a Webex presentation to a client who was interested in using Maple for a physics course in chaos. Of the two texts selected for the course, I had one on my own bookshelf. So I scanned Steven Strogatz' text Nonlinear Dynamics and Chaos (Addison Wesley, 1994) for topics that would profit from investigation with Maple.

One of the best things about growing up in the “Hood” is that it feels really good when you leave. I grew up in a neighborhood called Downsview in Toronto whose claim to fame used to be it was the home to the DeHavilland Aircraft company but today is more associated with ongoing issues of crime, poverty, and many other urban illnesses. So every time I hear that someone from the Hood did something great, I take notice and I take special pride. This is the story about...

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

Mea Culpa...

September 09 2010 Tom 4 724

A sign of a very successful period of work is the tally of how many email messages I’ve written that start with … “First, let me apologize for the delay in my response…” Yes, if you are the recipient of one of these notes from me, you’re probably more annoyed than pleased that I’m finding lots of very interesting things to fill up my ever-shrinking Outlook schedule. It’s been one heck of a summer, and I’m behind on countless...

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');

Consider the following C code:

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