Mathematics

Optimization algorithms seek to find the minimum values of mathematical functions in engineering. It's how engineers evaluate design trade-offs, assess control systems and how people find patterns in data.

One practical way to solve a difficult optimization problem is to first reduce it to a related but much simpler problem, then gradually add complexity back in, solving each new problem in turn and using its solution as a guide to solving the next one.

If only someone could find a way to characterize optimization theoretically. You know, optimize it.

Considering environmental effects such as a gravitational tidal force spread over a scale much larger than a galaxy cluster will be indispensable to explain the distribution and evolution of dark matter halos around galaxies, according to a comparison between theory and simulations by researchers at Kavli IPMU and collaborators.



The sex ratio in your community may affect what you're looking for in a relationship. Shutterstock

By Ryan Schacht, University of Utah and Monique Borgerhoff Mulder, University of California, Davis

Games have been test beds for new ideas in Artificial Intelligence (AI) since computers came on the scene and there have been significant milestones - Deep Blue sort of defeated Kasparov in chess and Watson sort of defeated Jennings and Rutter on Jeopardy! 

But solving a game is a lot tougher than defeating a player, though researchers in the Computer Poker Research Group at the University of Alberta in Canada say they have essentially solved heads-up limit hold'em poker

How people behave in a social network is somewhat mysterious, in the same way we can predict a presidential election with unprecedented accuracy but we can't predict how one person among the six percent of America that chooses a president will vote.

Decision-making often involves a confluence of opinions, decisions and behaviors of individuals influenced by their online networks, the same way they used to be shaped by their real-life networks.

A recent project set out to apply some math to help find some answers.


Ripple across social networks. Image credit: Laurel Papworth. Creative Commons


A young boy sits on the carpet, his feet disappearing into a giant pair of sweatpants he put on over his own clothes before loosely tying his ankles together.

He has taken the sweatpants off and is now trying to put them back on inside out without removing the ankle cuffs.

Yes, it can be done.



Holly Bernstein, who earned a PhD in mathematics at Washington University in St. Louis in 1999, watches him struggle for a bit and then says, “Remember the pants have more than one hole. You don’t necessarily have to put them back on the way you put them on in the first place.”

A desire to be part of the 'in crowd' could damage our ability to make the right decisions, according to a paper in the
journal Interface which claims that individuals have evolved to be overly influenced by their neighbors, rather than rely on their own instinct.

As a result, they believe, groups become less responsive to changes in their natural environment. So much for the wisdom of crowds.


When it comes to math, people mis-characterize themselves quite often. About 20 percent of the people who say they are bad at math score in the top half of tests while about 33 percent of people who say they are good at math score in the bottom half.


In the classical game theory match-up known as the Prisoner’s Dilemma, two prisoners kept isolated from each other are offered a deal: they can confess to a crime and if their accomplice remains silent the charges will be dropped in exchange for testimony against the other. If they both confess, they can both get early parole. If both remain silent, they get convicted of a lesser charge.