Mathematics

As Hank explains in a recent article, when he visits a Casino he plays the Roulette. His simple strategy consists in betting on a single colour, doubling the bet every time he loses; when he wins, he starts back with the minimum bet. Such a strategy is not going to make you rich, but no strategy does at the Roulette, especially the American one which has both a "0" and a "00" -two neutral numbers thrown in to enhance house odds. The idea of doubling every time is that eventually the colour you bet on is bound to appear, and you will win back all your fiches, plus one. Example: lose 1 - lose 2…

I had relatives visiting from out of town and, because they had never been to Las Vegas, we took a two day, one night,  short plane trip over the mountains.    Naturally, I won some money.   Is that because I am a mathematical genius?  No, everyone except the truly elite is going to lose money in a casino by knowing just enough probability to be dangerous while the truly stupid are going to be the foundation of any gambling town. Instead, I keep it simple and Roulette is what I do after I have had fun.  What, you say?  At 5.26 percent Roulette is not nearly…

They say the world is changing. Let’s check that out empirically. We might run a couple of sample surveys, to see how people’s behaviors or attitudes change between the two questionnaire mailings.  A colleague, however, suggests panel sampling. Which should we choose?  If we go with a panel, what kind of panel will cost-effectively measure the trend? Yes, these are leading questions, excuses for me to post a column about what my colleagues generously call “Phillips’ Law” of longitudinal sampling. People hear that and ask, “What the h*** is Phillips’…

If you want to solve big network security problems, sometimes it pays to think small - as in ants. A concept called 'swarm intelligence' adapts quickly to changing threats and it uses 'digital ants' to wander through computer networks looking for those threats, such as computer 'worms', those  self-replicating programs designed to steal information or facilitate unauthorized use of machines. When a digital ant detects a threat, it doesn't take long for an entire army of ants to converge at that location, which also draws the attention of human operators who step in to investigate.…

A new mathematical model of chronic wound healing could provide better guidance on how to tackle a major public-health problem - the estimated 6.5 million people in the USA who suffer from chronic wounds that can cause loss of limbs or even death. Ohio State University researchers are the first to publish a mathematical model of an ischemic wound – a chronic wound that heals slowly or is in danger of never healing because it is fed by an inadequate blood supply. Ischemic wounds are a common complication of diabetes, high blood pressure, obesity and other conditions that can be characterized…

Not really, but Paul Krugman is laying out some criticism of economics that's in the same spirit of my recent criticisms of networks and computational biology. "How Did Economists Get It So Wrong?": As I see it, the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth. Until the Great Depression, most economists clung to a vision of capitalism as a perfect or nearly perfect system. That vision wasn’t sustainable in the face of mass unemployment, but as memories of the Depression faded, economists fell back in love…

The story goes back to a conversation between me and Lothar in the summer of 2005. “Which instrument do you like the most Purushottam?“, He asked. “Piano”, I answered quickly. Though I played only guitar, piano was my favorite always. ” And why is that?”, he insisted. Why one likes anything is a different issue altogether and I am not going to dwell into that here. Important to this context was the answer I gave. “I like the pure sound, the notes, without mircrotones, not like violin, piano has a definite sound”. I was able to satisfy his ultra-inquisitive mind with this. I was relieved for…

Premier League clubs who have long-term managers are more successful than those who change their managers on a frequent basis, say business school researchers. Because there's nothing sports clubs want more than advice from  academics who examine past trends and draw conclusions  based on the fact that elite clubs fire people less. Using data from the inception of the Premier League in 1992 until 2004, which focuses on the short-term and long-term impact of manager change in the top flight of English football, they concluded that 'illusion effects', where the illusion of a short-…

I bought a pizza for the office today.  Don't get all excited and start thinking I am some aging hipster commie pinko, I am not.   I am just smart enough to make sure that in return for people enduring my jokes I  make sure they periodically get fed.   It's not like they can buy food with what I pay them. So that everyone would appreciate how magnanimous I am for dropping $5 on a Little Caesar's pizza, I wrote on my Faceyspaces and Tweetypages (what, you don't follow me on Faceypages and Tweetyspaces?  Here and here) ... Just bought pizza for the office. 74% of the…

Take a number. Take a second number. Add both together to produce a third. Again, add the last two numbers to produce the next. Repeat ad infinitum. What can be more boring? Well, the simple sequence you just generated has been studied for more than eight centuries, and continues to fascinate mathematicians, artists and numerologists alike. Countless research publications deal with Fibonacci sequences and related matters, there is a magazine dedicated to Fibonacci sequences, and every two years you can attend an International Conference on Fibonacci Numbers and Their Applications. In a recent…