Mathematics

How should scientists interpret their data? Emerging from their labs after days, weeks, months, even years spent measuring and recording, how do researchers draw conclusions about the results of their experiments? Statistical methods are widely used but our recent research in Nature Methods reveals that one of the classic science statistics, the P value, may not be as reliable as we like to think. Scientists like numbers, because they can be compared with other numbers. And often these comparisons are made with statistical analyses, to formalize the process. The broad idea behind all…

The concept of randomness has intrigued great minds for as long as history of great thinkers has been recorded.  From the nature of wind to drunks running into lampposts on their way home, scholars have been intrigued with making random predictable.  A group of chemists say they have challenged traditional interpretations of randomness by computationally generating random and mechanically rigid arrangements of two-dimensional hard disks, think pennies with no thickness, for the first time. In two dimensions, conventional wisdom held that the most random arrangements of pennies were…

Researchers focusing on a new way to discuss statistical mechanics have modeled "World War Z", an oral history of the first zombie war, to explore how an "actual" zombie outbreak might play out in the U.S.   Why model the mechanics of fictional zombies? "Modeling zombies takes you through a lot of the techniques used to model real diseases, albeit in a fun context," says Alex Alemi, a graduate student at Cornell University, who notes that it is a nice introduction to disease modeling in general, as well as highlighting techniques of statistical physics for measuring second-order phase…

By Ker Than,  Inside Science (Inside Science) -- Opinions rarely form in a vacuum. People are heavily influenced by the opinions of others in their social networks, whether they be real or virtual. Some people are not open to new ideas. These are the zealots, who proselytize an opinion -- the superiority of Apple products, for example, or skepticism about climate change -- in the hopes of convincing others, while stubbornly resisting being influenced themselves. Researchers studying the evolution of sentiments in a society, a field called opinion dynamics, have long been interested in…

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. This sequence of graphs illustrates the…

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. In the standard scenario for the formation of a cosmic structure, dark matter, which has an energy budget in the universe that is approximately five times greater than ordinary matter (e.g., atoms), first gathers gravitationally to form a crowded region, the so-called…

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 Popular wisdom and established evolutionary science hold that the sexes seek fundamentally different relationships: men want short-term, no-strings-attached relationships whereas women value longer-term, loyal partnerships. The explanation generally comes down to biological differences between men and women. Because women invest more in reproduction than men do – think pregnancy, morning sickness…

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.  Poker is a family of games that exhibit imperfect information, where players do not have full knowledge of past…

Origami: Paper folding may look like art, but it's all about the math. Mina, CC BY-NC-ND By Thomas Hull, Western New England University Origami is the ancient Japanese art of paper folding. One uncut square of paper can, in the hands of an origami artist, be folded into a bird, a frog, a sailboat, or a Japanese samurai helmet beetle. Origami can be extraordinarily complicated and intricate. The art of origami has been going through a renaissance over the past 30 years, with new designs being created at ever-increasing levels of complexity. It’s no coincidence that this rise in origami…

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…