Monday, January 31, 2011

Slavery, power and the myth of Miss Kitty

Like many anthropologists, Mark Auslander began his career working in a distant, exotic place. In his case, it was Zambia. But it was the experience of teaching at Emory’s original campus, in Oxford, Georgia, that “really shook things up for me,” he says.

He and his students took two tours of the town’s historic cemetery, where some of the early leaders of Emory are buried. One visit was guided by a conservative white member of the community, another by a local African-American.

“They gave us totally different tours,” Auslander says. “One guide emphasized the glories of Emory, by which he meant the white Emory. The other emphasized the long history of racial discrimination, that was visible in the cemetery.”

In a segregated area lay the grave of Catherine “Miss Kitty” Boyd, an enslaved woman who was owned by Methodist Bishop James Osgood Andrew, the first president of Emory’s board of trustees. Bishop Andrew’s ownership of Miss Kitty and other enslaved persons triggered the 1844 national schism of the Methodist Episcopal Church, presaging the Civil War.

“Everybody in Oxford had an opinion about Miss Kitty,” Auslander says. Bishop Andrew used to claim he was only an accidental slave owner, since all of his slaves had been inherited or acquired through his three marriages. Some conservative whites sympathized with Andrew’s view, and contended that Andrew offered Miss Kitty her freedom but she refused to accept it. But the term “accidental” rankled some members of the African-American community, who believed that Miss Kitty was the bishop’s mistress, and that she had no control over that fate.

“My students and I began to realize that we were in the middle of a very complex and exciting window to an important chapter in American history," Auslander says.

What was the truth behind conflicting versions of the story of Miss Kitty, that had been passed through families in Oxford for 160 years? Where did she come from, and what happened to her descendants?

The search for answers led to Auslander’s forthcoming book, “The Accidental Slaveowner: Revisiting a Myth of the American South.” He will give a public talk on the book at Emory's Oxford College on Wednesday, Feb. 2.

Auslander, who is now with Brandeis University, helped organized Emory’s upcoming conference, “Slavery and the University: Histories and Legacies,” which begins on Thursday, Feb. 3. The first conference of its kind, it will examine the impact of the enslavement of people of African descent on institutions of higher education.

Visit Emory Report, to hear the podcast of an interview of Auslander by Dana Goldman.

Related:
Legacies of slavery move into the light
Sociologists celebrate civil rights, diversity
Separate and unequal?

Thursday, January 27, 2011

A suprise dimension to adding and counting


The new finite formula for partition numbers is revealed beginning at 0:25:00 in the video. The explanation of how partition numbers are fractal begins at about 0:47:00.

Mathematician Ken Ono recently presented new breakthroughs in number theory that were centuries in the making. In the above video, you can watch Ono explain the first finite formula to calculate any partition number, and the discovery that partition numbers behave like fractals.

Ono gave the special hour-long lecture for a general audience at Emory on Jan. 21. Although the talk begins with the Count from Sesame Street, it quickly escalates to complex formulas, demonstrating why the simplest problems to state in number theory can be the hardest to solve.

Related: New theories reveal the nature of numbers

How do you count a number’s partitions, or the sequences of positive integers that add up to that number? It sounds easy, until you realize that the number 100 has more than 190,000,000 partitions.

If you were to try to write down all the partitions of the number 200, then add up how many there were, you would never finish. It would take you several lifetimes, and you probably wouldn’t arrive at the correct answer anyway.

The Mandelbrot set, above, is the most famous fractal of them all, and demonstrates the endlessly repeating patterns of forms in nature. Ono and his colleagues discovered a new class of fractals, one that reveals the endlessly repeating superstructure of partition numbers. Credit: Wikipedia Commons/Wolfgang Beyer.

Theories for partition numbers may seem esoteric, but they have many real world applications. “The rules of partition function played a role in the early development of computers,” Ono says. “The security of your emails and of your bank card also depend on partition function.”

Ono led a team of researchers to make the recent breakthroughs, including Jan Bruinier of the Technical University of Darmstadt, Amanda Folsom of Yale and Zach Kent of Emory. Their work was funded by the American Institute of Mathematics and the National Science Foundation.

Related:
How a hike led to a math 'Eureka!'
New theories reveal the nature of numbers

Thursday, January 20, 2011

New theories reveal the nature of numbers

A key creative breakthrough occurred when Emory mathematicians Ken Ono, left, and Zach Kent were hiking. As they walked, they noticed patterns in clumps of trees and began thinking about what it would be like to "walk" amid partition numbers.

By Carol Clark

For centuries, some of the greatest names in math have tried to make sense of partition numbers, the basis for adding and counting. Many mathematicians added major pieces to the puzzle, but all of them fell short of a full theory to explain partitions. Instead, their work raised more questions about this fundamental area of math.

Now, Emory mathematician Ken Ono is unveiling new theories that answer these famous old questions. (Click here to watch a video of Ono's lecture on the topic.)

Ono and his research team have discovered that partition numbers behave like fractals. They have unlocked the divisibility properties of partitions, and developed a mathematical theory for “seeing” their infinitely repeating superstructure. And they have devised the first finite formula to calculate the partitions of any number.

“Our work brings completely new ideas to the problems,” Ono says. “We prove that partition numbers are ‘fractal’ for every prime. These numbers, in a way we make precise, are self-similar in a shocking way. Our ‘zooming’ procedure resolves several open conjectures, and it will change how mathematicians study partitions.”

The problems of partition numbers "have long fascinated mathematicians," Ono says.

The work was funded by the American Institute of Mathematics (AIM) and the National Science Foundation. Last year, AIM assembled the world’s leading experts on partitions, including Ono, to attack some of the remaining big questions in the field. Ono, who is a chaired professor at both Emory and the University of Wisconsin at Madison, led a team consisting of Jan Bruinier, from the Technical University of Darmstadt in Germany; Amanda Folsom, from Yale; and Zach Kent, a post-doctoral fellow at Emory.

“Ken Ono has achieved absolutely breathtaking breakthroughs in the theory of partitions,” says George Andrews, professor at Pennsylvania State University and president of the American Mathematical Society. “He proved divisibility properties of the basic partition function that are astounding. He went on to provide a superstructure that no one anticipated just a few years ago. He is a phenomenon.”

Child’s play

On the surface, partition numbers seem like mathematical child’s play. A partition of a number is a sequence of positive integers that add up to that number. For example, 4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1. So we say there are 5 partitions of the number 4.

It sounds simple, and yet the partition numbers grow at an incredible rate. The amount of partitions for the number 10 is 42. For the number 100, the partitions explode to more than 190,000,000.

“Partition numbers are a crazy sequence of integers which race rapidly off to infinity,” Ono says. “This provocative sequence evokes wonder, and has long fascinated mathematicians.”

By definition, partition numbers are tantalizingly simple. But until the breakthroughs by Ono’s team, no one was able to unlock the secret of the complex pattern underlying this rapid growth.

The work of 18th-century mathematician Leonhard Euler (below) led to the first recursive technique for computing the partition values of numbers. The method was slow, however, and impractical for large numbers. For the next 150 years, the method was only successfully implemented to compute the first 200 partition numbers.

“In the mathematical universe, that’s like not being able to see further than Mars,” Ono says.

A mathematical telescope

In the early 20th century, Srinivasa Ramanujan and G. H. Hardy invented the circle method, which yielded the first good approximation of the partitions for numbers beyond 200. They essentially gave up on trying to find an exact answer, and settled for an approximation.

“This is like Galileo inventing the telescope, allowing you to see beyond what the naked eye can see, even though the view may be dim,” Ono says.

Ramanujan also noted some strange patterns in partition numbers. In 1919 he wrote: “There appear to be corresponding properties in which the moduli are powers of 5, 7 or 11 … and no simple properties for any moduli involving primes other than these three.”

The legendary Indian mathematician died at the age of 32 before he could explain what he meant by this mysterious quote, now known as Ramanujan’s congruences.

In 1937, Hans Rademacher found an exact formula for calculating partition values. While the method was a big improvement over Euler’s exact formula, it required adding together infinitely many numbers that have infinitely many decimal places. “These numbers are gruesome,” Ono says.

In the ensuing decades, mathematicians have kept building on these breakthroughs, adding more pieces to the puzzle. Despite the advances, they were unable to understand Ramanujan’s enigmatic words, or find a finite formula for the partition numbers.

“We were standing on some huge rocks, where we could see out over this valley and hear the falls, when we realized partition numbers are fractal,” Ono says. Photo by Zach Kent.

Ono’s “dream team” wrestled with the problems for months. “Everything we tried didn’t work,” he says.

A eureka moment happened in September, when Ono and Zach Kent were hiking to Tallulah Falls in northern Georgia. As they walked through the woods, noticing patterns in clumps of trees, Ono and Kent began thinking about what it would be like to “walk” amid partition numbers.

“We were standing on some huge rocks, where we could see out over this valley and hear the falls, when we realized partition numbers are fractal,” Ono says. “We both just started laughing.”

The term fractal was invented in 1980 by Benoit Mandelbrot, to describe what seem like irregularities in the geometry of natural forms. The more a viewer zooms into “rough” natural forms, the clearer it becomes that they actually consist of repeating patterns (see youtube video, below). Not only are fractals beautiful, they have immense practical value in fields as diverse as art to medicine.



Their hike sparked a theory that reveals a new class of fractals, one that dispensed with the problem of infinity for partition numbers. “It’s as though we no longer needed to see all the stars in the universe, because the pattern that keeps repeating forever can be seen on a three-mile walk to Tallulah Falls,” Ono says.

Ramanujan’s congruences are explained by their fractal theory. The team also demonstrated that the divisibility properties of partition numbers are “fractal” for every prime. “The sequences are all eventually periodic, and they repeat themselves over and over at precise intervals,” Ono says. “It’s like zooming in on the Mandelbrot set,” he adds, referring to the most famous fractal of them all.

An Atlanta traffic jam played a role in the final breakthrough of a formula.

But this extraordinary view into the superstructure of partition numbers was not enough. The team was determined to go beyond mere theories and hit upon a formula that could be implemented in the real world.

The final eureka moment occurred near another Georgia landmark: Spaghetti Junction. Ono and Jan Bruinier were stuck in traffic near the notorious Atlanta interchange. While chatting in the car, they hit upon a way to overcome the infinite complexity of Rademacher’s method. They went on to prove a formula that requires only finitely many simple numbers.

“We found a function, that we call P, that is like a magical oracle,” Ono says. “I can take any number, plug it into P, and instantly calculate the partitions of that number. P does not return gruesome numbers with infinitely many decimal places. It’s the finite, algebraic formula that we have all been looking for.”

The work by Ono and his colleagues resulted in two papers that will be available soon on the AIM website.

Related:
Ken Ono's public lecture on the new theories
How a hike in the woods led to math 'Aha!'

Thursday, January 13, 2011

Undersea cables add twist to DNA research

Just like underwater cables, DNA moves about in an aqueous environment, buffeted by currents and thermal energy. Understanding the stress mechanics of DNA could lead to clues about gene expression. Credit: istockphoto.com/rustycloud.

By Carol Clark

DNA is like an underwater cable. This pivotal idea occurred to mechanical engineer Sachin Goyal while he was a researcher at the University of Michigan. Working in the lab of Noel Perkins, Goyal was investigating the dynamics of steel cables mounted with acoustic sensors that are used by the U.S. military to monitor enemy submarines. The cables are attached to the seabed on one end, and to surface buoys on the other.

“Currents cause the buoys to rotate, twisting the cables,” explains Goyal, who is now a post-doctoral fellow in the Emory physics department. “The cables can get entangled and form loops that weaken them.”

The Navy needed to predict how the cables would bend and deform, or “hockle,” under different conditions. It’s the same principle as the compression load of a steel beam in a building, but instead of analyzing force applied to a straight rod, you have to factor in loops and twists.

Graphic: Noel Perkins, University of Michigan.

“It’s a mathematically challenging problem,” Goyal says. He developed a nonlinear theory for dynamic deformations of a rod, and the first computational model to simulate the mechanics of filament-like structures, to help engineers design optimal layouts for the undersea cables.

“I started thinking, ‘The kind of deformations that happen to underwater cables are the same that occur in DNA molecules,” Goyal recalls.

The revelation opened a whole new area of research for Goyal. Last year he joined the lab of Emory physicist Laura Finzi, who investigates the thermodynamics and kinetics of structural changes in DNA. Understanding these changes in DNA, the blueprints for all living organisms, is crucial to coming up with drug and vaccine design, and new technologies for genetic engineering and disease control.

Goyal’s expertise “fits perfectly within our group,” Finzi says. “Physics and chemistry are often called upon to investigate biological problems. It’s not so common to apply mechanical engineering, but it can provide new tools and insights.”
Click here to see the computer simulation of a cable tangling.

After simulating the dynamics of the deformation of an undersea cable, Goyal showed that the same principle applied equally well to DNA looping. The simulation captures the complete dynamics, not just a static behavior.

Just like underwater cables, DNA moves about in an aqueous environment, buffeted by currents and thermal energy. But while buckling and twisting are bad for underwater cables, they are much desired for DNA.

The entire human chromosome is a meter long, but it must pack inside a cell nucleus that is a few microns in diameter. The double-helical filament wraps over itself to form a superhelix so that it can fit into this microscopic space.

“DNA is always fluctuating, forming loops and straightening, which causes the DNA filament to become more or less accessible, turning genes on and off,” Goyal says. “My hypothesis is that you can predict where loops will form and where the DNA will be accessible if you understand the stress mechanics of DNA. Stress distribution may play a crucial role in gene expression.”
Sachin Goyal uses magnetic tweezers to tease out mechanical properties of DNA. Photo by Carol Clark.

The Journal of Physics recently published an Emory study focused on how one protein, known as C1, alters the mechanical behavior of DNA. “This protein can cling anywhere along DNA and as it clings, it causes the DNA to contract,” Goyal says. “The more proteins that bind to the DNA, the more contracted the DNA becomes.”

Previous research has shown that the C1 protein plays a role in sparking transitions between dormant and infectious states of viruses within a bacterial host. “We measured the contraction of the DNA, while measuring how much C1 was clinging to it,” Goyal explains. “One idea is that, by using such measurements, we could develop a model with which to explore when a pathogen might switch from a dormant to infectious stage.”

Related:
Biophysicists unravel secrets of genetic switch

Friday, January 7, 2011

Brain responds to 'art for art's sake'


By Quinn Eastman

What is art? Critics and historians have debated the question for years. Now Emory imaging research reveals that the ventral striatum, a region of the brain involved in experiencing pleasure, decision-making and risk-taking, is activated more when someone views a painting than when someone views a plain photograph.

The images viewed by study participants included paintings from both unknown and well-known artists such as Leonardo da Vinci, Paul Klee, Claude Monet, Pablo Picasso and Vincent Van Gogh, and photographs representing similar subjects.

The results are published in NeuroImage.

The ventral striatum is part of the "reward circuit," a set of regions of the brain involved in drug addiction and gambling, says senior author Krish Sathian, professor of neurology, rehabilitation medicine and psychology at Emory University School of Medicine.

The reward circuit also includes other parts of the brain such as the orbitofrontal cortex. Sathian emphasizes that the reward circuit is not just activated by experiences such as gambling or drug-taking, but is also involved in reinforcing behaviors under conditions of uncertainty, such as financial decision-making, for example.

Read more

Related:
Chimps mirror emotion in cartoons

Thursday, January 6, 2011

CDC turns into movie set for 'Contagion'


What's going on at the Centers for Disease Control and Prevention? Traffic backed up around Emory today as news cameras, soldiers and police swarmed around the CDC entrance.

A major pandemic? No, just a movie about one.

Filming for the Warner Brothers production "Contagion" will continue in the CDC/Emory area and other parts of metro Atlanta during the next few days. So you weren't hallucinating if you saw Laurence Fishburne strolling on Clifton Road. Other stars in the production include Matt Damon, Gwyneth Paltrow, Jude Law and Kate Winslet.



Steven Soderbergh is directing the thriller about the unraveling of society in the face of a deadly pandemic. The SARS outbreak of 2003 and the H1N1 pandemic of 2009 make "Contagion" a timely topic. It will be interesting to see how Hollywood portrays scientists racing to find a cure for an airborne virus that kills within days as panic spreads globally, amid ordinary people and world leaders.

An early draft of the script by Scott Burns, who also wrote "The Bourne Ultimatum," gets a thumbs up from a reviewer at "The Playlist," who writes that the plot is as much about how news spreads virally in the Internet age as it is about a spreading virus. Jude Law plays a crazed blogger.

Related:
From deadly flu to dengue fever, rising risks
Science and disasters in the movies

Wednesday, January 5, 2011

Mathematician eyes odds of Mega Millions


The bigger the jackpot, the longer the lines to buy lottery tickets. And when the jackpot gets really huge, people are more likely to splurge on 100 tickets. In this Fox Atlanta news video, Emory mathematician Skip Garibaldi gives his two cents on the odds of winning the $355 million Mega Millions jackpot, the second biggest in the lottery's history.

(You may have to hit "refresh" to get the video to appear. It's acting finicky.)

Related:
Lottery study zeros in on risk
The math of card tricks, games and gambling