Maplesoft Blog

The Maplesoft blog contains posts coming from the heart of Maplesoft. Find out what is coming next in the world of Maple, and get the best tips and tricks from the Maple experts.

Yesterday I watched a demonstration of Maple being applied to the modeling and simulation of the internal deformations of human bones. The researcher was a mathematician working primarily in the biomedical modeling fields. The actual technique was to utilize the symbolic mathematical power of Maple to formulate the necessary equation pieces for a finite element model (FEM) of the internals of the bone. The equations are then fed into the legendary FEM solver ABAQUS.

Due to the notoriously non-linear qualities of human flesh and bone, traditional formulation methods developed for modeling beams and metals simply do not work. So as in the case of so many impressive engineering applications, the power of Maple is being deployed in the formulation or the pre-solution phase of modeling and in doing so, previously infeasible models now become feasible.

That’s a mantra I need to have drummed into me, and perhaps tattooed on the inside of my car so I’m reminded every morning.  But I keep on making the same mistakes. 

 I seem to think that if I’ve “optimized” my portfolio with a few flashy calculations that I’ve done my due diligence, and the next stop is financial independence.  It’s the black box syndrome – trusting the output of a computer program without truly understanding the real issues.  Most portfolio analyses, for example, hinge on historical data, which of course doesn’t predict the sub-prime blow-up in the US or whether Brazilian coffee growers are on strike.  They’re all backward looking.

 However, in the absence of a neighbourhood scryer, historical analyses are a good indication of how to position a portfolio for the long term.

 Being a geek (however much I strenuously deny it), I tend leverage my tech skills wherever I can.  I wrote the attached worksheet to import stock quotes, including historical data, from Yahoo using the Sockets package.  Simply type in the appropriate NYSE stock tickers into the appropriate text boxes, check the quantities you want to download, and click the big gray button.

 All the stock quotes and historical data can be manipulated on the command-line and can be accessed via command-completion. 

 It then finds the best distribution of stocks in a portfolio by maximizing its Sharpe Ratio (through the Optimization package). 

The Sharpe ratio quantifies how effectively a portfolio of risky assets utilises risk to maximise return.  It’s defined as follows.

 

 

It essentially measures how effectively a portfolio uses risk to maximize return – the higher the ratio the better.  The expected portfolio return is predicted from historic data, the portfolio standard deviation is traditionally used as a proxy for risk, and the risk free return is the return that can be expected from a zero-risk investment (i.e. the interest on US Treasury Bills or the redemption yield on UK gilts).

What I find particularly fascinating is how Maple is now the centre of my technical desktop.  Through the combination of the interface and its math tools, I now use it for everything from the simplest calculations through to making wild guesses about my financial future.  If any of the developers are reading this, I want you to know there’s a lot riding on you...

Ruined your life?  Well, almost.  But now that you’re intrigued with my wild claim, let me explain.

The science of mathematics has a very long heritage.  The language of mathematics, as we recognize it today, is a bit younger – widely credited to François Viète, who introduced the first systematic algebraic notation in the last half of the 16th Century.

Along the way, over the course of many centuries, the power of mathematics increased steadily, through the contributions of many great men. 

One of the greatest pleasures of my job is meeting users and learning first hand of their achievements (hopefully with our products). Last week was a particularly eventful week and a distinct highlight was a visit our friends at the Canadian Space Agency (CSA) in Montréal.

Two very significant things happened last week. First, my son Eric turned 13. Second, I got a new car. These two milestones merged into a singularly great long weekend as Eric and did our very first father-son roadtrip to the great city of Cleveland. The car was the first new car my family had bought in about eight years, and as hard as I tried to maintain meaningful conversation with Eric through the many hours, I have to admit that my attention was frequently diverted to the car … thoughts of “hey … that’s a nice ride”, “so that’s what sport suspension feels like”, or “Yes Eric, that’s a very good question on the American election but … I wonder what that button does”.

As Maplesoft’s Chief Evangelist, I get countless opportunities to present the joys of Maple and our other products to people. Often, I’m the model corporate citizen and make sure I stay true to all of the key messaging that our Marketing folks force us to repeat … but if you actually experience one of my live presentations, you’ll notice that I often sneak in a whole slew of personal commentary and anecdotes on my 20 or so years with this technology … often stories that never make it to our official scripts. So as my inaugural blog post, I thought I’d start with what turns my crank when I have to present our products to the world. Here’s my Top 10 list of things that still impresses me to no end …

A little over ten years ago, I was shown a brief demonstration of Maple and I was astounded if not shocked by what it could do and my imagination immediately kicked into overdrive with ideas on how this unique technology could transform the way people work. My imagination has not settled down since.

These are exciting times for Maplesoft. With the introduction of an outstanding new release of Maple and a revolutionary technology MapleSim for modeling and simulation, we’re poised to launch a new generation of innovation and productivity for the engineering and mathematics community.

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