A Medical Mathematical Model

Yashtini says that she was drawn to this area of research because the ability to quickly solve a problem is key when we deal with real-world applications such as medical procedures.

Take for instance the magnetic resonance imaging scan, or MRI. A traditional MRI technique requires a patient to remain still for approximately 40 minutes and must be restarted if the patient makes even the slightest movement. Not only was this older MRI model uncomfortable for the patient, the MRI measurement often was not accurate enough. 

The algorithms developed by Yashtini drastically reduce not only the time needed for an MRI, but substantially improve the quality of images produced as well. 

“These new machines partially acquire data, then the missing data pixels are reconstructed and artifacts are removed afterward using optimization algorithms I developed,” Yashitini explains. “This process reduces the scanning time to less than five minutes, which allows the motion-related artifacts to be suppressed. It also lowers the side effects and costs for patients, which is the coolest part.”

Algorithms such as this can also be used to improve number approximations in images like biological cells, production line items, or people in crowds.

Counting approximations are complex problems for machine learning programs to solve, especially when there are several overlapping objects, objects with varying textures or when there is not a large enough data set with accurate boundary annotations. Many machine learning programs that currently exist are also often object-specific and require a time-consuming training process to operate. 

This problem led Yashtini and her collaborators at the Georgia Institute of Technology to develop a highly expedient,  geometry-free and training-free counting method that works for various objects.

“Efficiency and accuracy are crucial — whenever I see an optimization model coming from real-world applications, I naturally start thinking about ways to solve it quickly, or quicker than existing algorithms, while making sure the proposed methodologies are backed up with theoretical analysis and guaranteed convergence,” Yashtini says. 

This research also has applications in image colorization (coloring black and white images/videos), image denoising (eliminating noise and artifacts from images), matrix factorization, sparse reconstruction, and regressions. 

Mathematical Mentoring

Yashtini has passed on her passion to undergraduate and graduate students alike. Sanchi Gupta (C’24), said that Yashtini was accommodating and engaging throughout virtual learning.

“I loved the Calc II class so much that I decided to TA under Dr. Yashtini this semester, and it has been my pleasure working with her,” says Gupta. “Dr. Yashtini is a great teacher who goes above and beyond to help her students!”

Alexi Albert (G’21), who earned her Master’s in Mathematics from Georgetown, went out of her way to pursue courses taught by the professor. 

“Professor Yashtini taught a variety of numerical methods and facilitated our deep understanding of these methods by having us create algorithms for each in MatLab,” says Albert. “Knowing how to format this type of code has been an invaluable skill, and I’m very grateful to Professor Yashtini for her guidance and mentorship. She is a knowledgeable, kind and thoughtful professor, and I feel lucky to have been able to learn from her during my time at Georgetown.” 

Yashtini says that the support of her colleagues like Ruel Hector, R. Tiongson and Jill Brasky have been an immense help. 

“I am so grateful to work and research at Georgetown University and working with such great colleagues and talented students.”

Related News

Department Highlight – Mathematics & Statistics Professor Kimberly Sellers Creates Varied Research Opportunities for Students

The prestigious national scholarship – given to students who excel in mathematics, engineering and the natural sciences – has been awarded to three other Georgetown ������̳ students over the past six years. They include Patrick Mulcahey (C’19), and

“I am so honored and excited to have been selected as a 2020 scholar, and so thankful to everyone – especially my academic mentors and my parents – who have supported me over the years,” says Good. “I hope that this recognition of my research will afford me new opportunities to continue my training so that I can most effectively help people and advance scientific understanding through my work.”

Good plans to pursue a Ph.D. in biophysics and computational biochemistry after graduating from Georgetown to address questions of protein structure, function and design as an academic researcher in order to help other scientists develop tools to better understand diseases such as cancer, genetic diseases or viruses.

Working for Others

The rising senior spent her first, sophomore, and junior years working in professor lab, which focuses on intra-protein signal transduction mediated by allosteric interactions. 

“Lydia provides a numerical and computational approach to study how proteins receive and pass along signals,” says Maillard. “The results from her work focused on Protein Kinase A, may open new opportunities for the development of novel therapeutics.”

Good’s work specifically looks at applying statistical tools to traditional biophysical analysis methods. Good started her research as a collaboration with professor . 

“These new approaches enable more robust and detailed descriptions of the processes of protein interactions from data collected using optical tweezers,” she says.

Summer Research

The Goldwater recipient also earned an opportunity with the Research Experience for Undergraduates Program with the Rosetta Commons, a group of academic labs studying protein structure prediction using the Rosetta macromolecular modeling, earlier this year. She is spending this summer examining a new area of protein research through a lab at the University of Copenhagen in Denmark online due to the COVID-19 pandemic. 

Good’s research acumen has been recognized with numerous awards including the Clare Booth Luce Scholarship and Summer Fellowship, the and the Baker Scholars Fellowship. 

Enjoying Campus Life

When she is not in the lab, Good can be found dancing alongside her peers in the , where she also works as the student artistic director. Good is also an energy and water conservation team member with .  

This past season, she had the opportunity to choreograph her first original work for the company. Good says that dancing “not only helps me keep active and maintain balance in my life on campus, it engages a completely different but complementary side of my brain to my research.”

“It was a unique challenge that taught me not just about dance but about the process of reflecting, putting pieces and people together, and presenting work to a broader audience,” she continues. “I also value GUDC and GREEN for the amazing group of people from all sides of campus that I have met through these organizations, many of whom have become my closest friends at Georgetown.”

Mentoring, Matson, and Methane

A double major in mathematics and computer science, Matson wanted to merge these passions with research on climate change for her senior thesis.

“Climate change is the biggest threat to society and humanity that we are facing today,” says Matson. “It affects all disciplines, so it should be studied through interdisciplinary approaches instead of in isolation. By utilizing advancements in technology and computer science, we can better understand what is happening and fix it.”

 With the help of her advisor, professor who wrote the first-of-its-kind book Mathematics and Climate, Matson looked at previous studies that utilized satellite data to track methane emissions based on their locations. The two decided that this idea could be their jumping-off point.

“We chose to focus on methane as opposed to other greenhouse gasses like carbon dioxide because if its emissions are reduced, the resulting problems will go away more quickly than they would with other pollutants,” says Matson.

Making an Improved Model

The satellite data they used was readily available through an international effort, however, the data set itself was sparse. The satellite network tracking methane emissions covers the entire planet, but each satellite is responsible for a huge section of land, making it impossible to pinpoint exactly where large amounts of methane are being emitted. Despite these limitations, researchers are able to tell which areas produce more than others.

“You can look at the data and say ‘it looks like this section of the world has more emissions than that section right now,’ but you can’t get more specific than that,” says Engler. “Sally and I are working to create a better model that would use this same data to describe the emissions over space and time.”

Matson and Engler looked at the data available and charted the emissions recorded at each location individually over time. Simultaneously, they mapped emissions from all locations at one point in time. Matson and Engler used this data to create regression analyses that showed the temporal and spatial relationships in methane emissions around the globe more clearly than before.

Because of this improved data, future research examining the link between pollution and climate change can be refined, and better policies pinpointed at problem areas can be made.

Matson’s Next Steps    

Matson plans to continue her work on the intersection of climate change and technology after graduating from Georgetown. As a recipient of the 2020 Marshall Scholars Award, she will pursue a master’s degree in climate change at the University of East Anglia and a master’s degree in machine learning and machine intelligence from the University of Cambridge.

A proposal from Chris Ferris (C’20) and Sean Letendre (C’20) won first prize in its category at a hackathon hosted by the at the last month.

featured teams of students who submitted competing proposals to better secure elections and preserve democracy in the digital age. Judges included former Secretary of Defense Ash Carter, former campaign managers for Hillary Rodham Clinton and Mitt Romney, and officials from government agencies, technology firms, and think tanks.

in the Technical Method Project Design or Concept category, which required competitors to “Develop a project proposal or system design for a technical method to stop information operations from exploiting social media platforms.”

ACTIVE PARTICIPANTS

When Ferris and LeTendre heard about the Hackathon from alumna Sara Carioscia (C’17), they immediately saw an opportunity that could put their skills to good use at the epicenter of government and cybersecurity.

“We wanted to seize the opportunity to become active participants in the effort to hinder the spread of misinformation,” Letendre said.

“I feel news organizations and politicians have discussed the problem of information attacks damaging democratic systems at length, but have failed to propose and implement effective solutions,” Ferris added. “I was also attracted by the cash prizes.”

The two submitted a two-page concept proposal and were selected as one of three finalist teams that would travel to Cambridge, Mass., to present their ideas to the judges.

SOCIAL FACT CHECKING

Ferris and Letendre’s concept seeks to directly address the problem of unreliable or false “news” spreading over social networks without making a dramatic change to user experiences.

Titled “Social Fact Checking,” the concept encourages a large base of verified users to correct claims made in trending articles and posts, and then non-intrusively inserts these corrections into online content.

As Ferris and Letendre envision it, Social Fact Checking would allow people reading online content to see that a claim is possibly incorrect, click once to see a summary of the evidence against the claim, and click again to see direct links to the underlying sources of that summary.

“By allowing people to know a claim is contested and understand the evidence that contradicts the claim without having to disrupt their reading by going to an external site, our application prevents uninformed people who are concerned with the truth from being influenced by and sharing false information,” Ferris said.

Ferris and Letendre’s proposal finished ahead of finalists from the and . The team left with a greater appreciation for the work of cybersecurity professionals.

“We saw what it looks like for representatives of governments and corporations to discuss and collaboratively work towards solutions that defend democracy,” Letendre said.

The Georgetown team hopes to develop a prototype Social Fact Checking software over the next few months, then pitch it to an established media education organization like the .

CREATIVE SOLUTIONS

The Georgetown team credits their coursework for preparing them to compete in the Hackathon.

“The excellent computer science program allows students to develop technical and problem-solving skills and gives students experience working collaboratively on teams to solve problems,” Ferris said. “Having gone through some of this program helped me at the Hackathon.”

In addition to their computer science classes, Ferris and Letendre are pursuing majors in and , respectively. Ferris believes these interdisciplinary academic plans gave them an additional edge.

“In my government coursework, I have been encouraged to think about creative solutions to political issues,” Ferris said.

February 13, 2018&�Բ�����;—&�Բ�����;�ʰ��Ǵڱ�����ǰ��� and of the have organized a symposium “Mathematics of Planet Earth: Superbugs, Storm Surges, and Ecosystem Change,” for the of the American Association for the Advancement of Science (AAAS) at its annual meeting in Austin, Texas, next week.

ADDRESSING A BROAD AUDIENCE

The AAAS Annual Meeting is the nation’s largest general science assembly, drawing a broad spectrum of researchers — “from astronomy to sociology,” according to Engler — and a significant media presence.  The meeting is held every year and features plenary lectures, poster sessions, and approximately 150 topical 90-minute symposia.

Given the diverse interests of the audience, mathematics is usually presented through its applications.  “People tend to think that nothing new in mathematics has happened since 1900, and that’s not the case,” Kaper said.  “Mathematics is alive and well and finding more and more applications.” This year’s symposium theme chosen by the organizers is Mathematics of Planet Earth (MPE).

The symposium features Clint Dawson of the University of Texas at Austin, Corina Tarnita of Princeton University, and Glenn Webb of Vanderbilt University.  Each of the speakers will highlight how mathematical modeling can be used to predict climate events and environmental behavior.

SUPERBUGS, STORM SURGES, AND ECOSYSTEM CHANGE

Dawson uses mathematical models to predict how storm surges and rainfall will impact coastal land areas. His research helps coastal communities, like nearby Houston, better prepare for dangerous storms.

“These computational models are detailed enough to give you many scenarios of how a certain area could be overwhelmed with floodwaters, or whether a sea wall would protect an area,” Engler said. “You can’t do a laboratory experiment for a hurricane, but you can do a computer simulation.”

Tarnita researches vegetation patterns, focusing on dry ecological systems like savannahs and shrublands. Her models can be used to predict rapid changes in vegetation that indicate a potential shift to a desert climate.

“You can tweak the model and see what happens in response to changes in rainfall patterns over the next few decades — if they increase, decrease, or the frequency or seasonality changes, all of which could happen with climate change,” Engler said. “How will this affect the vegetation patterns?”

Webb’s models track the spread of infectious diseases through communities, focusing on the spread of the Zika virus — in both Rio de Janeiro and Houston — as well as influenza outbreaks.

“It’s looking at a spatial community,” Engler said. “[Webb] is modeling how Zika might start in one corner of one town and the way it spreads via mosquitoes, for example.”

CLIMATE MATH PIONEERS

While Kaper and Engler aren’t presenting themselves, they are no strangers to leadership roles in the field of climate mathematics.

After a distinguished career spent working in applied mathematics at Argonne National Laboratory and the National Science Foundation, Kaper joined the Georgetown faculty in 2008. He and Engler, a longtime Georgetown mathematics professor, soon began to explore climate mathematics.

“Climate is among the most important issues we face, and you don’t hear enough about it,” Kaper said. “It will affect our lives — if not my generation, certainly the younger generations.”

Shortly after leaving the NSF, Kaper helped found the Mathematics and Climate Research Network (MCRN), a group of 12 research teams from across the US with an international membership of well over 200, to create a community of mathematicians and geoscientists to study climate issues.

“It was a virtual community of people who didn’t know each other, who got together and used modern web communication tools, with occasional face-to-face meetings, to address mathematical issues related to climate,” Engler said.

Inspired by the MCRN, Kaper and Engler sought to bring a climate mathematics course to the Hilltop. Upon discovering a dearth of good literature, they published a textbook, Mathematics and Climate, which was published in 2014 by the Society for Industrial and Applied Mathematics (SIAM). They see climate mathematics as an exciting opportunity for classroom experience, due in part to the frequent tie-ins to real world events.

“This is an area where current events just constantly pop up,” Engler said. “It makes it very rewarding to teach.”

Kaper is Founding Chair and Engler the current Chair of the SIAM Activity Group on MPE.

The Fall 2016 semester has brought a number of passionate and qualified new instructors to Georgetown ������̳. Learn what they’re teaching, their research interests, and some of their extracurricular interests here. 

Department of Government

Luke Keele comes to the Hilltop as an associate professor at both the McCourt School of Public Policy and the Georgetown ������̳ department of government. An expert in statistical methods in the social and medical sciences, his research will focus on applying advanced statistics to the evaluation of labor market interventions, educational reforms and voter turnout. He has been published in the Annals of Applied Statistics, Psychological Methods, and the American Political Science Review (among others), and was most recently a member of the faculty at Penn State University. Keele is a graduate of Calvin ������̳ Grand Rapids (MI) and the University of Carolina at Chapel Hill, where he earned his Ph.D. in political science. He is married with one daughter and enjoys travel, project cooking, scuba diving and rock climbing in his spare time.

Department of Computer Science & Department of Linguistics

A self-identified “professional nerd,” Nathan Schneider joins both the computer science and linguistics departments from the University of Edinburgh, where he recently completed his postdoctoral fellowship. He leads interdisciplinary courses and research on the intersection of linguistics and computer science, specializing in computational linguistics and natural language processing — that is, using computational methods to study language and creating technology that can reason and process language. Nathan graduated from the University of California-Berkeley with a bachelor’s degree and from Carnegie Mellon with a Ph.D. He maintains a “collection of scholarly remarks on the mind-boggling versatility of the preposition ‘for.’”

Department of Psychology

Ian Lyons is an assistant professor of psychology focusing on cognitive neuroscience, specifically mathematical thinking and symbol representation. He received his Ph.D. in psychology from the University of Chicago, and most recently completed his postdoctoral fellowship at Western University in Ontario.
 

Department of Chemistry

Nag Gavvalapalli is a newly appointed assistant professor in the department of chemistry and the Institute for Soft Matter, Synthesis and Metrology. He attended University of Massachusetts Amherst and University of Illinois at Urbana-Champaign for his graduate and postdoctoral research, respectively. His research at Georgetown ������̳ focuses on the rational design and development of smart polymers and nanostructures. Gavvalapalli’s research is focused toward realizing novel electronic and photonic materials. Students in his research group are trained at the interfaces of polymer chemistry, organic chemistry, and nanoscience. To learn more about his research, please visit .
 

Department of Linguistics

Luke Plonsky joins the the ������̳ as assistant professor in the applied linguistics concentration. His primary teaching and research interests include second language acquisition and research methods. Plonsky is an associate editor of Studies in Second Language Acquisition, managing editor of Foreign Language Annals, and co-director (with E. Marsden & A. Mackey) of : A digital repository of Instruments for Research into Second Language Learning and Teaching. Plonsky has taught in the Netherlands, Puerto Rico, Spain, the U.S., and most recently in the U.K. at University ������̳ London. Plonsky received his Ph.D. in second language studies from Michigan State University in 2011. Learn more about him at .

Department of Mathematics and Statistics

Mark Meyer is assistant professor of statistics and a biostatistician. His first stint in Washington, DC was as an undergraduate at American University (Class of 2008) and as a post-baccalaureate fellow at the National Institutes of Health. After that, Mark completed his graduate work at Harvard University, earning his master’s in 2011 and doctorate in 2014, both in biostatistics. Previously, he was an assistant professor of mathematics at Bucknell University where he taught statistics. Currently, his research focuses on developing novel methodologies for analyzing functional and categorical data. Meyer collaborates with researchers in a wide variety of disciplines, including environmental health, epidemiology, developmental medicine, animal behavior, and political science. This fall, he will be teaching Categorical Data Analysis (MATH 657). In the spring, he will be teaching Bayesian Statistics (MATH 640) as well as developing and teaching a new course for undergraduates: Biostatistical Methods.

Department of English

Amanda Phillips comes from the University of California, Davis, where she was the IMMERSe postdoctoral fellow for the ModLab Digital Humanities Collaboratory. She received her Ph.D. as a Mellon/ACLS dissertation completion fellow in the department of English at the University of California, Santa Barbara, with an emphasis certificate from the department of feminist studies. Her broad research interests are in social justice in and around technoculture, popular media, and the digital humanities. More specifically, she writes about video games and feminist, queer, and critical race theory. This fall, she’ll be teaching Intro to Video Game Studies.

Phillips was born and raised in Tampa, Florida, and spent significant time in Houston, Texas, as an undergraduate at Rice University. She is coming to DC with her partner, Shyama, and their dog, Yakshi. She is a bicycle commuter and enjoys weightlifting in her spare time.

Department of Computer Science

Justin Thaler is a computer scientist who is interested in the development of scalable algorithms that are efficient in both theory and practice. He is particularly interested in questions like: How can one design algorithms for analyzing massive datasets, even if there is so much data the the algorithm can store only a small fraction of it? How can one offload the processing of a massive dataset to a cloud computing service, and obtain a guarantee that the cloud is doing the processing correctly? Under what circumstances can machines make accurate predictions based on past experience or data?

Prior to joining the ������̳, Thaler spent two years as a research scientist at Yahoo Labs in New York City. Before that, he was a research fellow at the Simons Institute for the Theory of Computing at UC Berkeley. He received his Ph.D. in 2013 from the theory of computation group at Harvard University.

Department of Theology

Brandon Dotson is associate professor of Buddhist studies. Before coming to Georgetown, he spent six years in Munich, where he led a research group. Before that, he spent nine years at Oxford University, where he did his graduate studies and a postdoctoral fellowship. Originally from Southern California, his work concerns ritual, narrative, and cosmology and the interaction of Buddhist and non-Buddhist traditions in the Tibetan cultural area. In particular, he works closely with Tibetan Dunhuang manuscripts to explore the history and culture of the Tibetan Empire (7th to 9th centuries CE). At Georgetown ������̳ he teaches courses on Buddhism, Tibetan Buddhism, and the Problem of God.