Friday, January 17, 2020

Emory mathematician ignites acclaim for one of year's top discoveries

"Pure mathematicians are like poets and philosophers," says Hao Huang, with an illustration of the sensitivity conjecture. "We're trying to get at larger truths, in the simplest way possible." (Photo by Kay Hinton)

By Carol Clark

A European heat wave provided the final spark Emory mathematician Hao Huang needed to crack one of the most important, and baffling, open problems in theoretical computer science.

Discover Magazine named Huang’s proof of the sensitivity conjecture one of the “Top 50 Science Stories that Matter” for 2019, due to the simplicity of the proof and the conjecture’s implications for processing information. And Popular Mechanics called Huang’s achievement one of “The 10 Biggest Math Breakthroughs” of the year.

Mathematicians and computer scientists had grappled with the sensitivity conjecture for three decades without success. Huang, an assistant professor of mathematics, became intrigued by it in 2012.

“I spent a lot of nights thinking about this problem,” Huang recalls, estimating that he pondered it off and on over the years for hundreds of hours. “I eventually became obsessed with it.”

In late June, Huang’s wife, Yao Yao, a mathematician at Georgia Tech, was an invited speaker at a conference in Madrid, Spain. Huang tagged along, with the idea that he would spend a few days sightseeing while his wife attended the meeting.

A heat wave swept through Europe, however, and Madrid temperatures reached 105 degrees. “I had to stay in my hotel, in an air-conditioned room,” Huang says.

During this forced confinement, Huang doubled down on the sensitivity conjecture. A key idea emerged. “I finally identified the right tool to solve it,” he says.

The sensitivity conjecture relates to Boolean data, which maps information in a true-false, or 1-0 binary. Boolean functions are one of the most basic of discrete subjects — like numbers, graphs or geometric shapes, Huang explains. Boolean functions also play an important role in complexity theory, as well as in the design of circuits and chips for computers.

There are many complexity measures of Boolean functions and almost all of them were known to be mathematically related. The only unknown case, the so-called sensitivity of a Boolean function, measures how sensitive the function is when changing one input at a time.

Mathematicians proposed the sensitivity conjecture in 1994 concerning this unknown case, but no one had been able to prove it.

Finally, sitting in a Madrid hotel room to escape the stifling heat, Huang came up with a simple algebraic method for proving the conjecture.

“I was quite excited,” Huang recalls. “And then I calmed down and started checking the work.”

His wife also checked the proof when she returned to the hotel from the conference.

Once he was convinced of its accuracy, Huang posted the work on his homepage.

Mathematicians and computer scientists from around the world lauded the proof. “Amazingly short and beautiful,” wrote Gil Kalai, a mathematician at the Hebrew University of Jerusalem. Claire Mathieu of the French National Center for Scientific Research described Huang’s proof as “a precious pearl” in Quanta Magazine.

The list of people who tried to solve the sensitivity conjecture and failed “is like a who’s who of discrete math and theoretical computer science,” Scott Aaronson, from the University of Texas, told Quanta.

Huang believes the method he developed may have the potential to be applied to other combinatorial and complexity problems important to computer science. He is happiest, however, about the crisp elegance of the work.

Often, he notes, mathematical proofs can go on for 100 pages or more and be too complex for all but the most specialized of readers to grasp. In contrast, Huang’s proof consists of two pages and every college level math major can understand it.

“Pure mathematicians are like poets and philosophers,” Huang says. “We’re not focused on whether our work has an immediate impact. We’re trying to get at larger truths, in the simplest way possible.” 

It’s a completely different mindset from an engineer, he adds. “Engineers want to make things work, however possible,” he says. “Theoretical mathematicians want to understand how things work in their most natural way.”

A native of Shantou, a coastal city of in southern China, Huang says his love of math emerged in his childhood. He attended a high school specialized in mathematics and later graduated from Peking University.

Many of his classmates went on to careers in technology or finance, but Huang prefers academia and its focus on pure math. “I love the flexibility of it,” he says. “All I need is a pen and paper. I can work on a train or in an airplane — or in a hotel room.”

Huang is not resting on his laurels following his proof of the sensitivity conjecture. “There are a lot of elegant theorems and beautiful conjectures out there that we don’t yet know how to prove,” he says.

Related:
Emory mathematician to present proof of the sensitivity conjecture
Mathematicians revive abandoned approach to the Riemann Hypothesis

Wednesday, January 8, 2020

'Bilingual' molecule connects two basic codes for life

The new molecule holds the potential for diverse biomedical applications, says Emory chemist Jennifer Heemstra (right), senior author of the paper. She is shown in her lab with graduate student Colin Swenson, first author of the paper. (Photo by Kay Hinton)

By Carol Clark

The nucleic acids of DNA encode genetic information, while the amino acids of proteins contain the code to turn that information into structures and functions. Together, they provide the two fundamental codes underlying all of life.

Now scientists have found a way to combine these two main coding languages into a single “bilingual” molecule.

The Journal of the American Chemical Society published the work by chemists at Emory University. The synthesized molecule could become a powerful tool for applications such as diagnostics, gene therapy and drug delivery targeted to specific cells.

“Much like a translator enables communication between two people from different regions of the world, we envision that our bilingual molecule will enable us to mediate new forms of communications between nucleic acids and proteins in the cellular environment,” says Jennifer Heemstra, associate professor of chemistry at Emory University and senior author of the study. 

Nucleic acids store information in an “alphabet” of four bases, known as nucleotides. Peptides and proteins use an entirely different alphabet, made up of 20 different amino acids.

“The nucleic acid language is easy to speak, but kind of limited,” Heemstra says. “While the protein language is incredibly complex and difficult to predict. Both of these molecules have developed exquisite properties over billions of years of evolution.”

Previously synthesized molecules have focused on the properties of either nucleic acids or amino acids. The Emory researchers wanted to harness the powers of both information systems within a single molecule.

The challenge was enormous, drawing on techniques from organic chemistry, molecular and cellular biology, materials science and analytical chemistry. The researchers built a protein scaffold and then attached functioning fragments of nucleotides and amino acids to this framework.

“The two different codes needed to be synthesized separately and then brought together into the scaffold,” says Colin Swenson, first author of the paper and a graduate student in the Heemstra Lab.

The resulting bilingual molecule is stable, made of inexpensive materials, and highly generalizable, giving it the potential for diverse biomedical and nanotechnology applications. “It’s like a programmable, universal adaptor that brings proteins and nucleic acids together,” Heemstra says. “We hope that other researchers are inspired to think about different ways that it might be applied.” 

The Emory chemists are now exploring using the bilingual molecule for targeted drug delivery to particular cells. “It’s essentially a stimuli-sensitive container,” Heemstra says. “We’ve demonstrated that it can bind to drug molecules. And it’s programmable to fall apart in the presence of specific RNA molecules that are more abundant in cancer cells.”

Related:
Chemists teach old drug new tricks to target deadly staph bacteria
DNA 'origami' takes flight in emerging field of nano machines