Mathematics

A new way of looking at a previously abandoned mathematical model might help astronomers study and accurately identify an exotic clan of gravitational waves. The waves in question come from small black holes or neutron stars in extremely elongated orbits around vastly larger black holes, says Dr. Lior Burko, an assistant physics professor at The University of Alabama in Huntsville (UAH). "This reopens an area of research that was closed several years ago." The exotic gravitational waves are generated (as predicted by general relativity theory) when an orbiting compact object changes speed,…

Have you ever been trying to solve a Sudoku puzzle and been gripped by a sinking feeling that maybe you were stuck with a lemon? That maybe the puzzle you are struggling with actually has no solution at all and, if you do find a solution, how can you be sure it's the only one? What if half an hour ago you had written 5 instead of 3---would you then have gone down a path to a completely different solution? The authors of a new study use tools from the branch of mathematics called graph theory to systematically analyze Sudoku puzzles. They also find that analyzing Sudokus leads to some unsolved…

'Tis the season—the real estate season—and though this one isn't shaping up to be the boomer of two years ago, or even the desperate sell-off of last summer, people will nevertheless be buying houses. If you are one of these people, read on. It's a buyers market this year (or so my real estate agent tells me), but which house is right for you? Use this equation to find out—it works surprisingly well. As you will notice, this equation is really just a way to quantify your opinions—and add some objectivity to the house-buying process! How important is something to you? Well, if you think a…

27 moves? They don't need no stinking 27 moves. Northeastern University Computer Science professor Gene Cooperman and graduate student Dan Kunkle set out to do what no one clamored for - solving any Rubik's Cube configuration in 26 moves, a new record. Welcome to the family of cosets. “The Rubik's cube is a testing ground for problems of search and enumeration,” says Cooperman. "Search and enumeration is a large research area encompassing many researchers working in different disciplines – from artificial intelligence to operations. The Rubik's cube allows researchers from different…

A data-driven computational approach developed by a University of Illinois statistician is revealing secrets about inner Earth and discovering unique gene expressions in fruit flies, zebra fish and other living organisms. "Using mathematical concepts from inverse scattering and modern statistics, we let the data 'speak,' and automatically generate an appropriate model," said Ping Ma, a professor of statistics at the U. of I. and lead author of a paper describing the technique that has been accepted for publication in the Journal of Geophysical Research. To study features deep within Earth,…

Professionally speaking, things in David Damanik's world don't line up – and he can prove it. In new research, Damanik and colleague Serguei Tcheremchantsev offer a key proof in the study of quasicrystals, crystal-like materials whose atoms don't line up in neat, unbroken rows like the atoms found in crystals. Damanik's latest work focused on a popular model mathematicians use to study quasicrystals. The research, which was 10 years in the making, proves that quasicrystals in the model are not electrical conductors and sheds light on a little-understood corner of materials science. "This is…

Mathematicians and number buffs have their records. And today, an international team has broken a long-standing one in an impressive feat of calculation. On March 6, computer clusters from three institutions – the EPFL, the University of Bonn and NTT in Japan -- reached the end of eleven months of strenuous calculation, churning out the prime factors of a well-known, hard-to-factor number that is a whopping 307 digits long. "This is the largest 'special' hard-to-factor number factored to date," explains EPFL cryptology professor Arjen Lenstra. (The number is 'special' because it has a…

Lately they've been dropping like flies—Imus, Rosie, Rumsie. Who's next? Gonzales? Wolfowitz? And then there's Alec Baldwin—he doesn't, technically, have anything to resign from, but what are the chances his career can recover from the temper tantrum he left on his 12-year old daughter's phone? What about a more esoteric resignation candidate like Cheney? Is there any hope? Well, it turns out there are some factors that correlate pretty well with a person's likelihood of resigning. Of course, the egregiousness of the crime matters, but what really counts is public outrage—how pissed are…

I originally wrote this equation for an interview on the PRI radio program Fair Game, but we got to chatting and ran out of time, so I thought I'd blog it as well. Let me first say that I think it would be a lot of fun to invade Trinidad. While I mean no disrespect to Trinidad, I'm fairly certain it would not be an overly cumbersome task for the U.S. military (even extended as they are). And the exit strategy would be obvious: after Carnival, we come home. We could make it a yearly event — invade Trinidad, party for a couple weeks, and then bring the troops home. Talk about a morale booster…

The primary source of doubt about studies of global warming, economics and medical issues is how well the scientists compiling the data know their statistics. The European Science Foundation’s three-year SACD network developed new methods for extracting key structural features within the data including outlying values that may be particularly significant within increasingly large and complex data sets. "Outliers often indicate the most interesting data points, like polluted areas for environmental data, or irregularities in online monitoring of patients," said SACD chair Christophe Croux.…