Mathematics

Adult humans possess some mathematical abilities that are unmatched by any other member of the animal kingdom but there is increasing evidence that the ability to count sets of objects nonverbally is a capacity that humans share with other animal species.

In PLoS Biology, Elizabeth Brannon and Jessica Cantlon discuss how humans and nonhuman animals share a capacity for nonverbal arithmetic. The researchers tested monkeys and college students on a nonverbal arithmetic task in which they had to add the numerical values of two sets of dots together and choose a stimulus from two options that reflected the arithmetic sum of the two sets.


Monkeys perform addition like humans.

The journal Experimental Mathematics, started in 1992, publishes “formal results inspired by experimentation, conjectures suggested by experiments, descriptions of algorithms and software for mathematical exploration, [and] surveys of areas of mathematics from the experimental point of view.” The founder wanted to make clearer and give more credit to an important way that mathematicians come up with new ideas. As the journal’s statement of philosophy puts it, “Experiment has always been, and increasingly is, an important method of mathematical discovery.

One of the foundations of Einstein's Special Relativity is that no particular frame of reference is better than any other - whether you're sitting on the couch or barreling through space on a rocket, physics doesn't change. On the other hand, as many physics undergrads learn, choosing the right reference frame can simplify your homework problems a lot.

Thanks to Einstein, physicists know that the world looks different depending on how fast you're moving.

As the weather cools and Halloween approaches, creaks in the stairs and scary stories become more believable -- but not to physics professor Costas Efthimiou.

The laws of physics and math debunk popular myths about ghosts and vampires, according to a paper published by Efthimiou and Sohang Gandhi last year.

Using Isaac Newton's Laws of Motion, Efthimiou demonstrates that ghosts would not be able to walk and pass through walls. Basic math disproves the legend of humans turning into vampires after they are bitten, Efthimiou explains, because the entire human population in 1600 would have been wiped out in less than three years.


Doomed by mathematics

Scientists at the U.S. Department of Energy's Brookhaven National Laboratory have developed a method for correlating the results of microscopic imaging techniques in a way that could lead to improved understanding, diagnosis, and possibly treatment of a variety of disease conditions, including Alzheimer's disease. The Laboratory has filed a U.S. provisional patent application for the invention.

The invention is essentially a micron-scale metallic marking grid upon which scientists place their samples - biological tissues or inorganic samples such as minerals - prior to imaging with different methods.

A group of scientists, led by mathematicians, has taken on the challenge of building a common model of immune responses. Their work will radically improve our understanding of the human immune system by allowing all the scientific disciplines working on it to have a common reference point and language.

The mathematicians will investigate how the different cellular components of the immune system work together and devise a theoretical and computational model that can be used by immunologists, mathematicians, computer scientists, physicists and engineers.

The model promises to help a multi-disciplinary research community work together to bring about medical advances for patients.

A University of Leicester mathematician has been working with scientists in Japan and The Netherlands to develop a new technique that produces accurate mathematical models of the actual behaviour of nerve (neural) cells. Developing such models requires detailed information about the dynamics of components responsible for the spike generation in the cell.

The main barrier between mathematical modelling and reality is that the most of intrinsic variables of living cell are not available for direct observation. Dr Ivan Tyukin and his colleagues developed a method for automatic reconstructing of hidden variables describing the cell dynamics using only the recordings of evoked electric activity of the cell.

So, you've seen the WSOP on ESPN—big money, big personalities, big bluffs. But what these highlight reels forget to mention is the fact that, at the highest level, there's method behind the blood-pumping madness. Behind every good bluff is a strong foundation of numbers. And here it is: the equation that defines when to pull the trigger, even if you're holding three-six offsuit.

Plug your numbers into this equation (or into the attached spreadsheet calculator) to calculate the percentage that you should bluff. Note—this works well for a specific situation: No Limit Texas Hold' Em, just after seeing the flop.

Rather than waxing poetic, it seems best to look at the variables in order:

In yacht racing, a one percent difference in boat resistance leads to a gain or loss of more than 30 seconds in a match race.

Computational fluid dynamics research done by the winning Swiss Alinghi America's Cup syndicate led to gains of 2-5 percent in drag reduction on appendages like the keel, bulb and winglets, absolutely essential gains when you take into consideration that opponent Emirates Team New Zealand won two of the first three races but lost when the wind was more difficult.

Advanced numerical methods have come a long way, it seems.

The 2007 America's Cup was the first time every major contender used applied mathematics and computer simulation. As competition gets more fierce, the optimization of every part becomes more important.

New Scientist has written an article stating that new quantum technology can run a routine called Shor’s algorithm and that means the most dangerous threat posed by quantum computing, the ability to break the codes that protect our personal data, is now a step closer to reality.

Worse, they report this feat has been performed by not one but two research groups, acting independently; one led by Andrew White at the University of Queensland in Brisbane, Australia, and the other by Chao-Yang Lu of the University of Science and Technology of China, in Hefei. Both teams have built laser-based quantum computers that can implement Shor’s algorithm and defeat today’s most common encryption systems.

Full article: http://www.newscientist.com