#MathStatMonth: Getting to the ‘square root’ of security [New content added twice weekly]

It’s Mathematics and Statistics Awareness Month aka #MathStatMonth, and at the National Science Foundation, we are taking this opportunity to explore some #NSFmath at the root of all kinds of security that keep our nation and world a safer place. From threat detection to cyber security, throughout the month, we will spotlight various #NSFfunded mathematical and statistical research that is fundamental to myriad security issues. Keep checking back here to see how #NSFmath helps keep our nation more secure.

Mathematics is the underpinning for so much (maybe all!) of the science involved in what we think of as security and preparedness. Whether it’s protecting the electric grid or preparing for a potential bioterrorist attack, mathematicians are involved and playing a key role in these issues. Photo credits clockwise, starting from top left corner: Peter Craine, Senior Airman Walker from Kadena Air Force Base, and gargantuen all via Wikimedia Commons.

Calculating solutions to combat Zika

Photo credit: Centers for Disease Control

It’s a puzzle where lives are at stake. Figuring out how to curb Zika and minimize death and illness related to this virus projected to return in force as temperatures rise and populations of the Zika-bearing mosquito (A. aegypti) resume.

But math is playing a key role in solving this puzzle. Mac Hyman, is one such mathematician who has conducted more than 15 years of mathematical research related to vector-borne diseases. Hyman is currently working with other scientists to develop a model that would track how to fight A. aegypti with bacteria, at least until researchers develop a Zika vaccine.

“We are modeling a new control mechanism based on infecting mosquitoes with the bacteria Wolbachia,” said Hyman, an NSF-funded researcher at Tulane University who also received funding from the National Institutes of Health (NIH). “The idea is to create a Wolbachia epidemic in A. aegypti mosquitoes so they are less capable of transmitting the virus. Wolbachia already occurs naturally in 25–75 percent of the insect population, but not in A. aegypti. Infecting the mosquitoes with this bacteria can reduce their ability to lay viable eggs and shorten their lifespan by a day or two.”

By using mathematical modeling and analysis, we can learn about transmission and control of disease that may not be immediately clear through data collection involving those infected. Consequently, collaborations between mathematicians and biologists allow understanding to be advanced more quickly.

Tool against bioterrorism that helps fast-track treatment/vaccines

Anthrax (shown above) is considered to be one of several bacteria that pose potential as a bioterrorist weapon. Mathematicians like Erick Matsen develop algorithms that help develop treatments and vaccines faster, which would be critical in a bioterrism event. Photo credit: Centers for Disease Control and Prevention‘s Public Health Image Library

While the idea of bioterrorism likely conjures up images of scientists in HAZMAT suits scrutinizing vials of smallpox, anthrax or other highly contagious disease, Erick Matsen pursues his work armed with simply a computer. That’s right — not a germ in sight.

A mathematician at the Fred Hutchinson Cancer Research Center in Seattle, Matsen employs math to decipher the way antibodies “block infection and neutralize viruses.” “If I get a cold, my body has a large population of antibodies that bind to the virus reasonably well,” Matsen said. “But the amazing thing is that there’s this further mutation and selection process driven by the body’s own mechanisms which iteratively improves the binding of the antibodies. In the selection step the antibodies are checked to see if they fit better than previous ones. If they do, they survive.”

The body then stores these highly refined antibodies in “immunological memory,” he says, which is the reason you don’t get the same flu twice, and also the foundation for the work he does.

And while this may sound a lot more like biology than math, mathematicians like Matsen work with something called phylogenetic trees that compare molecular sequence data such as DNA to infer evolutionary histories both on the viral and immune system side of the equation. This allows him to garner valuable evolutionary understanding of many biological systems, develop algorithms, and prove theorems that help us understand these mutation and selection processes. It’s this work that assists clinical trials to develop treatments and vaccines with new, cutting-edge math — something that’s as useful for developing cancer treatments as it is for speeding up a treatment or vaccine in response to a bioterrorism attack.

“Along the way, we get to do some really interesting math problems that no one has ever even thought about,” Matsen said. “recently we discovered some new integer sequences, which in combinatorics is a little discovering a new species.”

Developing and analyzing mathematical models to ensure secure electric power

Mathematicians work with power engineers to identify and address vulnerabilities. Photo credit: U.S. National Archives and Records Administration

On Aug. 14, 2003, 50–55 million people in the U.S. Northeast and Midwest, as well as Canada’s Ontario province, were left in the dark after a high-voltage powerline in Northern Ohio had a run-in with overgrown trees. The event ultimately caused a cascade of power failures that in some cases were not resolved for nearly a week. Considered the biggest blackout in North American history, it’s the kind of disaster power engineers work every day to prevent. Alongside them are a few mathematicians like Barry Lee from Southern Methodist University.

Lee realizes that the power grid of today and the emerging grid of the future will be far different from those in 1965, and with but with those changes come new vulnerabilities. “One of the biggest vulnerabilities arises from instability of the grid. Moreover, a more recent vulnerability is cybersecurity because the power grid is online,” he said.

Additionally, deregulation means more utility companies now “manage” the grid, so if they don’t share data describing the state of their managed area, and there’s no centralized control center, basic shared procedures to prevent a wide spread of instabilities will be hard to enact. Additionally, renewable energies such as solar cells or wind turbines contribute to the grid, creating yet another variable to understand the ebb and flow of electricity.

Consequently, Lee’s NSF-funded mathematical research develops models that include large systems of equations describing the angles and voltage magnitudes in the flow of electricity. By introducing cutting-edge mathematics and new algorithms to collaborating power engineers, he’s able to help them better prepare for potential surges and system ruptures and maintain a stable power grid. “One of the biggest parts to our challenge is understanding each other’s technical languages,” Lee said. “But the goal here is to understand the instability/stability of the grid and to have methods for solving power-grid problems much more quickly, even in real-time.”