Following the people and events that make up the research community at Duke

Category: Mathematics Page 1 of 7

Modeling Biology: Ruby Kim’s Research on the Math of Physiological Cycles

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What lies at the intersection of mathematics and biology? Freshly-minted math PhD Ruby Kim and her work on mathematically modeling human dopamine cycles.

Ruby Kim, recent Duke PhD graduate

Kim’s work has centered around her creation of a math model to predict how a person’s dopamine levels ebb and flow over the course of a day “to understand the general mechanics of how disruptions in the (biological) clock lead to disruptions in dopamine.”

She said there is a pretty long history of mathematicians using differential equations to see how different clock genes and proteins change over the course of a day’s circadian cycle. Yet, no previous models have connected the circadian clock – controlled by the brain’s suprachiasmatic nucleus – to dopamine levels. And Kim tells me that work suggesting dopamine changes throughout the day are likely controlled by the internal circadian clock itself is “relatively new.”

The first step in Kim’s work was validating scientists’– or “experimentalists,” as Kim dubs them –  hypotheses about dopamine and dopaminergic enzyme cycling.

Many physiological processes are controlled via circadian rhythms and the internal clock in humans, as well as other organisms.

“But I’d like this work to help experimentalists go one step further and be able to test out hypotheses more easily.” For example, Kim says that her model has the potential to reveal other fascinating phenomena, such as how drug treatments or different genetic mutations may impact circadian rhythm or dopamine. This is thanks to the multifaceted layers of Kim’s model.

“From a mathematical perspective, the math model is very interesting. It has a lot of interesting dynamics,” she says. “Not only does it show nice, 24-hour rhythms, it shows both steady state behavior… but then also behavior that’s really wild – something called quasi-periodic behavior, where the internal clock is significantly different than the external 24-hour light-dark cycle.”

“This leads to oscillatory behavior that’s not periodic,” she says. These sorts of quasi-periodic behaviors have been observed in experiments and misunderstood, but they can be computed.

Kim emphasized the experimental and clinical implications of her work. Dopamine is involved in learning and motivation and is also linked a plethora of psychiatric conditions like Parkinson’s, ADHD, and schizophrenia. “Patients with these conditions often also experience circadian disruptions,” Kim says. “That’s a pretty big symptom.”

Kim began her academic career in her home state of California at Pomona College as a pre-med math major. “I had always been intrigued by human physiology. And math was one of the subjects I was also pretty drawn to. I just didn’t appreciate it much because throughout high school and the beginning of undergrad, I didn’t see any direct applications,” Kim told me.

The marriage of her love for math with her intrigue in biology actually began at Duke when Kim attended a mathematical biology workshop during the summer after her sophomore year. “I had never heard of math biology before that.”

After working on a brief project to model sleep apnea in infants at the workshop, Kim returned to California and took up math modeling courses in her following semesters of undergrad. One of her professors, Ami E. Radunskaya, PhD, was extremely supportive and introduced Kim to a lot of “cool biological problems.” Kim went on to do research with Radunskaya, modeling tumor-immune interactions. This experience, Kim says, “kind of just threw me into academia.” The project gave way to an undergraduate thesis with Radunskaya that analyzed the long-term behavior of this tumor growth and treatment model.

Radunskaya then suggested that Kim pursue grad school. “I kind of applied on a whim,” Kim said, “It wasn’t something I had specifically imagined for myself.” Kim mentioned how no one from her home community had really ever gone to grad school and so it was not something she had ever “explicitly” thought about before.

Using mathematics to fight cancer | Department of Mathematics | University  of Washington
An abstract of Radunskaya’s work on mathematical modeling and understanding tumor-immune interactions to address cancer.

In her search for a graduate program, Kim applied to math programs, as well as those that were interdisciplinary. “I ended up choosing Duke because I really liked my advisor,” Kim told me. While Kim’s advisor Michael Reed, PhD “does a lot of interesting math,” Kim wanted to work with him because math isn’t his focus – understanding “really complex biological systems using mathematical language is.”

“A lot of times you see people who do things at the intersection of math and biology that are more motivated from a mathematical standpoint … that’s just not what I’m interested in personally. I’m very interested in finding an interesting biological problem and then applying whatever mathematical tools I have.”

While at Duke, Kim was foundational to founding the university’s chapter of the Association for Women in Math (AWM). During her undergrad, Kim “had a really great experience with AWM,” finding both a community of women mathematicians and a network of women professors who were involved in the chapter.

At Duke, there wasn’t a chapter “but quite a few people who were interested in starting and being part of one.” This organization, which is open to people of any gender identity, heads mentorship programming that brings undergrads, grad students, postdocs, and professors together, organizes conferences, and contributes to their central focus of community building in math.

Outside of her research, Kim spends most of her free time taking care of foster pups, which she describes as “extremely rewarding but also very tiring.” Her most recent foster, a four-month-old puppy, eavesdropped on our interview as he took a nap.

This fall, Kim will begin a post-doc with the University of Michigan’s math department as she “wanted to keep studying circadian rhythms with faculty who are really great in that area.”

Post by Cydney Livingston, Class of 2022

“Brains are Weird… and the World is Difficult”

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Institute for Consumer Money Management, and Duke University’s Center for Advanced Hindsight.

Intending to do the right thing doesn’t always lead to actually doing it, a tendency formally known as the “intention-behavior gap.” We can intend to go to bed early and still go to bed late. We can want to exercise and still choose not to. We can recognize the importance of saving extra money and still choose to spend it instead. So why is it so hard to change our behavior? Because, says Jonathan Corbin, Ph.D., “brains are weird” and “the world is difficult.”

Corbin is a senior behavioral researcher at the Center for Advanced Hindsight at Duke University. The Center for Advanced Hindsight recently partnered with NOVA Labs, Thought Cafè, and the Institute for Consumer Money Management to create the NOVA Financial Lab, a group of financial literacy games targeted at adolescents and emerging adults. In each game, players practice managing money while taking care of a pet. You may never have to sneak a cat into a concert or prepare a retirement plan for a dog in real life, but you will need to understand concepts like budgeting, interest, and debt. “What we hope people start to do,” Corbin says, “is really think about, ‘What decisions should I make now to make better decisions later?’”

Essentially, “Money spent now is money that can’t be spent later.” As intuitive as that might seem, “The way we think about money is relative, and it’s not linear.” When you’re already spending thousands of dollars on a car, for instance, an extra five hundred dollars for a feature you may or may not need “feels like a very small amount of money,” but in a different situation, its value can seem higher. How many times, Corbin points out, could you go out to eat with five hundred dollars?

The three games combine financial literacy with behavioral science to explore why people make the decisions they do and how they can start to make better ones.
Source: https://advanced-hindsight.com/wp-content/uploads/2022/03/CAH-NOVA.pdf

There are three games: Shopportunity Cost, Budget Busters, and Exponential Potential. (“One of the people from PBS helped us come up with these cute names,” Corbin says.) They each involve different skills, but they all focus on “financial literacy from a behavioral science perspective.” Players have to contend with both external obstacles and common behavioral biases to make financial decisions for a pet. “I always choose the dog,” Corbin adds, “but I understand other people might choose the cat.” (I chose the cat.)

The first game, Shopportunity Cost, focuses on short-term financial planning. It involves dressing a pet up like a person in order to sneak them into a concert for the night. “You have to make decisions that optimize the pet’s happiness while also being able to make it to the concert and back home,” but you have a limited amount of money to spend. If you spend too much money too soon, you’ll run out, but if you’re too frugal, your pet won’t enjoy the evening. As goofy as the concert scenario is, it introduces players to an important concept known as opportunity cost, which refers to the potential benefits we miss out on when we choose one alternative over another. Say you’re debating between a $50 outfit and a $30 one. The opportunity cost of choosing the more expensive outfit is $20, but shoppers don’t always consider that. “Opportunity cost neglect is the simple idea that when we’re faced with financial decisions, we tend not to consider alternative uses for that money.” Reframing the $30 outfit as “a $30 dress that I’m okay with plus 20 extra dollars” that could be spent elsewhere might lead you to choose the cheaper outfit. Or it might not. “Sometimes you want the $50 outfit, and that’s perfectly fine… but a lot of the time that might not be the right decision.” Like many things, taking opportunity cost into account is a balancing act. “We shouldn’t obsess over every possible opportunity that there is,” Corbin cautions, but “consider[ing] opportunity costs can lead to better financial decisions.”

Budget Busters, meanwhile, involves medium-term planning. Players have to manage checking, credit, and savings accounts while caring for their pet over a six-month period. Along with purchasing essential and non-essential items to attend to their pet’s basic needs and happiness, players have to contend with unforeseen circumstances like medical emergencies. The game introduces people to the 50-30-20 rule, a budgeting concept that involves devoting 50% of income to essentials, 30% to non-essentials, and 20% to savings. Budget Busters also explores the principle of mental accounting, the idea that aside from formal budgets, we have “categories in our head” that change our perception of money. “Let’s say you get birthday money from your relative. That money tends to be a different kind of spending money to you than money you get from your paycheck,” Corbin explains, because “money feels different in different contexts.” 

There are parallels in Budget Busters. Sometimes players receive unexpected windfalls like gifts or prizes. (My cat won $40 for being “Best in Show” at the local pet pageant.) Players get to decide whether to use the extra money on a “fun” item for their pet or put it into savings. Corbin says “gift money” is a classic example of a misleading mental account. “We tend to overspend… because it feels like it’s not even our money in a way.” In reality, though, money has “fungibility,” meaning it’s “exchangeable… across any account.” In other words, “money is money,” regardless of where it comes from.  A $10 bill, for instance, can be exchanged for two fives without changing its value. (Non-fungible tokens, or NFTs, lack this property. “You can’t exchange the picture of a cat you bought from the internet for Chipotle.”) Like Shopportunity Cost, Budget Busters focuses on both traditional financial concepts and common behavioral tendencies that affect decision-making. “None of these things are necessarily bad,” Corbin emphasizes, “but they’re things that one should be aware of… when that natural proclivity may be swaying them in the wrong way.”

Budget Busters, which focuses on monthly budgeting, also encourages players to look closely at discounts when shopping. “Sometimes the discount that looks really good from a  percentage-off perspective isn’t actually the better discount” in terms of overall budgeting and total amount of money saved, Corbin warns.

The last game, Exponential Potential, explores concepts like compound interest, debt, and investment. The premise of the game involves traveling back in time to balance debts and investments. The goal is to make your pet a millionaire. By showing players how investment decisions can affect future net worth, the game seeks to increase understanding of processes involving exponential growth. Exponential Potential introduces the concept of exponential growth bias. According to Corbin,  “We tend to underestimate things that grow exponentially.” He cites the coronavirus pandemic as an example: “Even the people who were making the graphs of Covid’s growth… it’s really hard for them to figure out how to show that to people.” Log-transformed graphs are one option, but they can be deceptive by making the slope look flatter. Similarly, when dealing with exponential growth in the financial world, “People are going to underestimate how badly they’re going to get burned” by debt, but they may also underestimate how much they’ll benefit by saving for retirement.

With compound interest, for instance, “The interest gets applied both to principle and to interest from the last time, and that’s where exponential growth happens.” In the game, players have the opportunity to adjust how much money to put toward paying off debts, investing, and saving for retirement each month. Then they travel decades into the future to see how their decisions have affected their pet’s net worth.  “We’re hoping that that kind of feedback allows you to think through… what you might have done wrong and try to correct,” Corbin says. Once again, though, raw numbers aren’t the only factor at play. “We just want people to understand what the optimal way to do this is, and if there’s a better way for them to do that psychologically, that’s fine.” Debt account aversion, for example, refers to the fact that people want to have fewer debt accounts, meaning they are often eager to pay off accounts in full when they can. Some financial advisers suggest that “because they think it’ll get the ball rolling and you’ll be more likely to pay off the next one.” According to Corbin, there isn’t a lot of evidence for that, and sometimes paying everything off at the outset isn’t ideal. For instance, “It is optimal to start thinking about retirement as soon as you can… but if you’re delaying putting money into retirement because you’re so concerned with your student loan debt,” that can be problematic. Still, Corbin understands the appeal of closing debt accounts. “I am risk-averse, which means if I have a debt I’m probably going to put more money toward that debt that I necessarily should given what the interest rates are and what I could potentially make by investing that money instead.” Financially speaking, “There’s a decent likelihood that I should just pay the minimum on my mortgage… [but] I’ve decided I’m willing to trade off those future gains for the peace of mind that if something goes wrong… I’ll be ahead on my mortgage payment.” Even in Exponential Potential, the right choices aren’t always clear-cut. Corbin describes it as a “sandbox approach” where players are given more opportunity to play around. “This is the trickiest game because there’s no perfect answer for anything,” he says. “Everything has risk.”

Another bias that can affect our financial decisions is known as present bias, the tendency to discount the future in favor of the present. Corbin offers the everyday example of staying up too late. “Nighttime Me wants to stay up and read…. Morning Me is going to be really ticked off at Nighttime Me when they’re exhausted and don’t want to get up.” Research suggests that people can have a harder time identifying with their future selves. That can easily affect our financial decisions, too. “I’m going to let future me worry about that. That guy. Whoever that is.” However, “If you can get people to identify more with that person,” they can sometimes make better decisions. Ultimately, “The game isn’t trying to force people to become investment robots.” We are biased for the present because we live in it, and that’s normal. The purpose of the game is simply “to nudge people… to worry just a little more about the future.”

“Money is basically for safety, security, and happiness,” Corbin says. The ultimate objective is to balance needs, wants, and savings to achieve those three goals both in the present and the future.

By Sophie Cox
By Sophie Cox

Undergraduate Researchers William He and Annie Wang Dig Deeper into Hypergraphs

Like most things during the height of the pandemic, research that could be conducted virtually was conducted virtually. And that’s why, although juniors William He and Annie Wang have been working together on a research project since last September, they’ve never actually met in person.

He, a Math major from Houston, and Wang, a Computer Science and Math double-major from Raleigh, both work in the lab of Professor Debmalya Panigrahi, where the focus is on research in theoretical computer science, particularly graph algorithms. Wang and He did work on hypergraphs, and, after I asked them to explain what hypergraphs were in the most elementary terms (I am not a Math major), they went back and forth on how exactly to relay hypergraphs to a lay audience.

Annie Wang

Here is what they landed on: hypergraphs are essentially generalizations of normal graphs. In a normal graph, there are edges –each edge connects two points. There are also vertices – each point is a vertex. But in a hypergraph, each edge connects multiple points.

He and Wang were looking at a generalization of graph reliability – if all edges disconnect at a certain probability, what is the probability that the graph itself will break down because crucial edges are disconnecting?

William He

Their research adds to existing research on maximum flow problems, which Wikipedia tells us “entail finding a feasible flow through a flow network to obtain the maximum possible flow rate.” In a landmark paper written by T.E. Harris and F.S. Ross in 1955, the two researchers formulated the maximum flow problem using an example of the Soviet railroad and considering what cuts in the railroad would disconnect the nation entirely – and what cuts could be made with little impact to railway traffic flow. 

Maximum flow problems are a core tenet of optimization theory, used widely in disciplines from math to computer science to engineering. You may not know what mathematical optimization is, but you’ve seen it in action before: in electronic circuitry, in economics, or unsurprisingly, used by civil engineers in traffic management.

It’s expected to be incredibly difficult to exactly calculate the target value of He and Wang’s question. They landed on an approximation that they know is far from the exact calculation, but still brings them closer to understanding hypergraph connectivity more fully.

The process

So what draws them to research? For He, it’s like an itch. He describes that “sometimes I’ll be watching a movie, and then thirty minutes in I’m thinking about a possible solution to a math problem and then I can’t focus on the movie anymore.” You can’t get on with things until you scratch the itch, but the best part to him is when things finally start to make sense. For Wang, research is just plain fun. She enjoys learning about algorithms and theorems, and she loves the opportunity to work with professors who are at the forefront of their field.

After Duke, He wants to pursue a PhD, likely in theoretical computer science, while Wang is still weighing her options – whether she wants to go into academia or industry. While He came into Duke as a prospective Economics major, in quarantine especially he realized just how much he enjoyed math for the sake of itself.

Wang, similarly, thought she would want to pursue software engineering, but she’s slowly realizing that she likes “solving the problems within the field – problems that I need a PhD to solve.” The magic of research, for her, is that “you’re solving problems that no one has answers to yet.” And wherever the future takes both of them, she says that in doing research, even at the undergraduate level, “you feel like you’re pushing the boundary a tiny bit, and that’s a cool feeling.”

Post by Meghna Datta, Class of 2023

A Puzzling Saga – Meet Duke Math’s Breakout Star!

When I think of crosswords, I think of young and old alike gathered around a couch, scribbling away on a freshly arrived newspaper on a clear Sunday morning. When I think of math, I think of passionate professors covered in chalk dust from a hard day’s work of etching out complicated Greek symbols and numbers on a huge blackboard. These two visions had always been comfortably separate from each other (disjoint sets, if you will) – until I met Dr. Adam Levine.

Meet Duke’s Adam Simon Levine – who shares his name with a pop star, and is a math and crossword rockstar in his own right.

Levine is an Associate Professor in the Department of Mathematics at Duke who studies low-dimensional topology, surfaces, knots and manifolds, using something called Heegaard Floer homology. But apart, from his incredible passion for his field, numerous grants and tongue-twister-esque research interests, Levine has one accomplishment that sets him apart.

He published a crossword puzzle in the New York Times on Sept. 25!

In our Zoom conversation, Levine was bright, chirpy and incredibly excited to talk about his unique love for crosswords and how he’s kept his hobby alive even under the pressures of academic life. As a teenager he loved working on puzzles like Scrabble, playing around with words and etymology, and of course, crosswords. As he grew older, he continued to be fascinated by words.

As an undergrad taking a History of Life class at Harvard, Levine learned about the the impact site of the asteroid that wiped out the dinosaurs, the Chicxulub crater. His first thought was, “That’s a fantastic word– that would make the perfect crossword entry!” His fascination with the word would stay alive for years, until it became the seed entry (the word that anchors the puzzle) for his first crossword to be published in the Times. His love for wordplay through the years is clear, from a self-composed song on Heegaard Floer homology, to a sonnet summary of his PhD thesis.

Watch Levine’s self-composed song here.

Levine continued to solve puzzles as he earned his multiple graduate degrees in mathematics, and began publishing his own puzzles a few years on his aptly named blog – Knotty Grids. Crosswords have been a fun and necessary hobby for him – a way to de-stress or take his mind off his academic work. He thinks it is an important example to set for undergraduate students hoping to pursue a career in math – to show them that it is possible to be “full human beings” and have diverse and unique hobbies, interests and a life outside of your research.

Levine often intertwines his puzzles with his primary interest. Some of his puzzles are “themed” – with “Tying Up Loose Ends” built around topological concepts, and the math-y “Indivisible” which was published in The Mathematical Intelligencer. His personal favorites, however, delve into the meta-puzzle genre with “The Queen’s Gambit” and “A Series of Unfortunate Events.”

Levine’s crossword grids are very literally inspired by his daily work with knots.

When I talked to him shortly after the NYT puzzle appeared, Levine was still visibly excited. He compared the puzzle-publishing journey to that of submitting his mathematical research to academic journals – tedious, long and not very fast-moving. Having submitted the crossword to the newspaper more than a year ago, he heard back from them early this year, at which point they began editing and working on the final publication.

As Levine spoke about the editing process, he brought up an issue that has been important to him – diversity in the puzzle world. Because most crosswords have been written by white men, clues and answers are often tilted towards what that demographic considers common knowledge, and minority and female creators have remained a very small voice. Erasure of their identities is common, and  Levine related a firsthand experience. His clue for “ROBIN” was “the first Black woman to host Jeopardy.” But it was initially edited to be a reference to the bird.

Levine says he pushed back on the parts of the puzzle that were important to him, and was glad with the final published result.

He says he was amazed by the outpouring of support and congratulations he received after the crossword came out. His parents were “really pumped,” family excited, and colleagues incredibly surprised to see his name in print (on a non-academic paper). Unfortunately, the weekend that the crossword was published, his undergraduate students were cramming for a midterm scheduled that Monday, which Levine figures might be the reason some of his crossword-fanatic students seem to have missed his big moment of glory.

In the following week, I spoke to one of Levine’s academic advisees and other Duke students passionate about puzzles, who shared an initial shock and an immediate subsequent joy in the Blue Devil puzzle representation that this publication debuted.

 While Levine has no imminent plans of writing another NYT puzzle, he continues to write for his personal blog. Hopefully, his unique journey inspires students and faculty from different fields and of varied backgrounds to contribute, create and participate, helping make his dream of a diverse puzzle world a reality.

Post by Nidhi Srivaths, Class of 2024


New Blogger Shariar Vaez-Ghaemi: Arts and Artificial Intelligence

Hi! My name is Shariar. My friends usually pronounce that as Shaw-Ree-Awr, and my parents pronounce it as a Share-Ee-Awr, but feel free to mentally process my name as “Sher-Rye-Eer,” “Shor-yor-ior-ior-ior-ior,” or whatever phonetic concoction your heart desires. I always tell people that there’s no right way to interpret language, especially if you’re an AI (which you might be).

Speaking of AI, I’m excited to study statistics and mathematics at Duke! This dream was born out of my high school research internship with New York Times bestselling author Jonah Berger, through which I immersed myself in the applications of machine learning to the social sciences. Since Dr. Berger and I completed our ML-guided study of the social psychology of communicative language, I’ve injected statistical learning techniques into my investigations of political science, finance, and even fantasy football.

Unwinding in the orchestra room after a performance

When I’m not cramped behind a Jupyter Notebook or re-reading a particularly long research abstract for the fourth time, I’m often pursuing a completely different interest: the creative arts. I’m an orchestral clarinetist and quasi-jazz pianist by training, but my proudest artistic endeavours have involved cinema. During high school, I wrote and directed three short films, including a post-apocalyptic dystopian comedy and a silent rendition of the epic poem “Epopeya de la Gitana.”

I often get asked whether there’s any bridge between machine learning and the creative arts*, to which the answer is yes! In fact, as part of my entry project for Duke-based developer team Apollo Endeavours, I created a statistical language model that writes original poetry. Wandering
Mind, as I call the system, is just one example of the many ways that artificial intelligence can do what we once considered exclusively-human tasks. The program isn’t quite as talented as Frost or Dickinson, but it’s much better at writing poetry than I am.

In a movie production (I’m the one wearing a Totoro onesie)

I look forward to presenting invigorating research topics to blog readers for the next year or more. Though machine learning is my scientific expertise, my investigations could transcend all boundaries of discipline, so you may see me passionately explaining biology experiments, environmental studies, or even macroeconomic forecasts. Go Blue Devils!

(* In truth, I almost never get asked this question by real people unless I say, “You know, there’s actually a connection between machine learning and arts.”)

By Shariar Vaez-Ghaemi, Class of 2025

Introducing: The Duke Space Initiative

NASA

Engineers, medical students, ecologists, political scientists, ethicists, policymakers — come one, come all to the Duke Space Initiative (DSI), “the interdisciplinary home for all things space at Duke.”

At Duke Polis’ “Perspectives on Space: Introducing the Duke Space Initiative” on Sept. 9, DSI co-founder and undergraduate student Ritika Saligram introduced the initiative and moderated a discussion on the current landscape of space studies both at Duke and beyond.

William R. & Thomas L. Perkins Professor of Law Jonathan Wiener began by expressing his excitement in the amount of interest he’s observed in space at Duke. 

One of these interested students was Spencer Kaplan. Kaplan, an undergraduate student studying public policy, couldn’t attend Wiener’s Science & Society Dinner Dialogue about policy and risk in the settlement of Mars. Unwilling to miss the learning opportunity, Kaplan set up a one-on-one conversation with Wiener. One thing led to another: the two created a readings course on space law — Wiener hired Kaplan as a research assistant and they worked together to compile materials for the syllabus — then thought, “Why stop there?” 

Wiener and Kaplan, together with Chase Hamilton, Jory Weintraub, Tyler Felgenhauer, Dan Buckland, and Somia Youssef, created the Bass Connections project “Going to Mars: Science, Society, and Sustainability,” through which a highly interdisciplinary team of faculty and students discussed problems ranging from the science and technology of getting to Mars, to the social and political reality of living on another planet. 

The team produced a website, research papers, policy memos and recommendations, and a policy report for stakeholders including NASA and some prestigious actors in the private sector. According to Saligram, through their work, the team realized the need for a concerted “space for space” at Duke, and the DSI was born. The Initiative seeks to serve more immediately as a resource center for higher education on space, and eventually as the home of a space studies certificate program for undergraduates at Duke. 

Wiener sees space as an “opportunity to reflect on what we’ve learned from being on Earth” — to consider how we could avoid mistakes made here and “try to do better if we settle another planet.” He listed a few of the many problems that the Bass Connections examined. 

The economics of space exploration have changed: once, national governments funded space exploration; now, private companies like SpaceX, Blue Origin, and Virgin Galactic seek to run the show. Space debris, satellite and launch junk that could impair future launches, is the tragedy of the commons at work — in space. How would we resolve international disputes on other planets and avoid conflict, especially when settlements have different missions? Can we develop technology to ward off asteroids? What if we unintentionally brought microorganisms from one planet to another? How will we make the rules for the settlement of other planets?

These questions are vast — thereby reflecting the vastness of space, commented Saligram — and weren’t answerable within the hour. However, cutting edge research and thinking around them can be found on the Bass Connections’ website.

Earth and Climate Sciences Senior Lecturer Alexander Glass added to Wiener’s list of problems: “terraforming” — or creating a human habitat — on Mars. According to Glass, oxygen “isn’t a huge issue”: MOXIE can buzz Co2 with electricity to produce it. A greater concern is radiation. Without Earth’s magnetosphere, shielding of some sort will be necessary; it takes sixteen feet of rock to produce the same protection. Humans on Mars might have to live underground. 

Glass noted that although “we have the science to solve a lot of these problems, the science we’re lagging in is the human aspects of it: the psychological, of humanity living in conditions like isolation.” The engineering could be rock solid. But the mission “will fail because there will be a sociopath we couldn’t predict beforehand.”

Bass Connections project leader and PhD candidate in political science Somia Youssef discussed the need to examine deeply our laws, systems, and culture. Youssef emphasized that we humans have been on Earth for six million years. Like Wiener, she asked how we will “apply what we’ve learned to space” and what changes we should make. How, she mused, do prevailing ideas about humanity “transform in the confines, the harsh environment of space?” Youssef urged the balancing of unity with protection of the things that make us different, as well as consideration for voices that aren’t being represented.

Material Science Professor, Assistant Professor of Surgery, and NASA Human System Risk Manager Dr. Dan Buckland explained that automation has exciting potential in improving medical care in space. If robots can do the “most dangerous aspects” of mission medical care, humans won’t have to. Offloading onto “repeatable devices” will reduce the amount of accidents and medical capabilities needed in space. 

Multiple panelists also discussed the “false dichotomy” between spending resources on space and back home on Earth. Youssef pointed out that many innovations which have benefited (or will benefit) earthly humanity have come from the excitement and passion that comes from investing in space. Saligram stated that space is an “extension of the same social and policy issues as the ones we face on Earth, just in a different context.” This means that solutions we find in our attempt to settle Mars and explore the universe can be “reverse engineered” to help Earth-dwelling humans everywhere.

Saligram opened up the panel for discussion, and one guest asked Buckland how he ended up working for NASA. Buckland said his advice was to “be in rooms you’re not really supposed to be in, and eventually people will start thinking you’re supposed to be there.” 

Youssef echoed this view, expressing the need for diverse perspectives in space exploration. She’s most excited by all the people “who are interested in space, but don’t know if there’s enough space for them.”

If this sounds like you, check out the Duke Space Initiative. They’ve got space.

Post by Zella Hanson

A New Algorithm for “In-Betweening” images applied to Covid, Aging and Continental Drift

Collaborating with a colleague in Shanghai, we recently published an article that explains the mathematical concept of ‘in-betweening,’in images – calculating intermediate stages of changes in appearance from one image to the next.

Our equilibrium-driven deformation algorithm (EDDA) was used to demonstrate three difficult tasks of ‘in-betweening’ images: Facial aging, coronavirus spread in the lungs, and continental drift.

Part I. Understanding Pneumonia Invasion and Retreat in COVID-19

The pandemic has influenced the entire world and taken away nearly 3 million lives to date. If a person were unlucky enough to contract the virus and COVID-19, one way to diagnose them is to carry out CT scans of their lungs to visualize the damage caused by pneumonia.

However, it is impossible to monitor the patient all the time using CT scans. Thus, the invading process is usually invisible for doctors and researchers.

To solve this difficulty, we developed a mathematical algorithm which relies on only two CT scans to simulate the pneumonia invasion process caused by COVID-19.

We compared a series of CT scans of a Chinese patient taken at different times. This patient had severe pneumonia caused by COVID-19 but recovered after a successful treatment. Our simulation clearly revealed the pneumonia invasion process in the patient’s lungs and the fading away process after the treatment.

Our simulation results also identify several significant areas in which the patient’s lungs are more vulnerable to the virus and other areas in which the lungs have better response to the treatment. Those areas were perfectly consistent with the medical analysis based on this patient’s actual, real-time CT scan images. The consistency of our results indicates the value of the method.

The COVID-19 pneumonia invading (upper panel) and fading away (lower panel) process from the data-driven simulations. Red circles indicate four significant areas in which the patient’s lungs were more vulnerable to the pneumonia and blue circles indicate two significant areas in which the patient’s lungs had better response to the treatment. (Image credit: Gao et al., 2021)
We also applied this algorithm to simulate human facial changes over time, in which the aging processes for different parts of a woman’s face were automatically created by the algorithm with high resolution. (Image credit: Gao et al., 2021. Video)

Part II. Solving the Puzzle of Continental Drift

It has always been mysterious how the continents we know evolved and formed from the ancient single supercontinent, Pangaea. But then German polar researcher Alfred Wegener proposed the continental drift hypothesis in the early 20th century. Although many geologists argued about his hypothesis initially, more sound evidence such as continental structures, fossils and the magnetic polarity of rocks has supported Wegener’s proposition.

Our data-driven algorithm has been applied to simulate the possible evolution process of continents from Pangaea period.

The underlying forces driving continental drift were determined by the equilibrium status of the continents on the current planet. In order to describe the edges that divide the land to create oceans, we proposed a delicate thresholding scheme.

The formation and deformation for different continents is clearly revealed in our simulation. For example, the ‘drift’ of the Antarctic continent from Africa can be seen happening. This exciting simulation presents a quick and obvious way for geologists to establish more possible lines of inquiry about how continents can drift from one status to another, just based on the initial and equilibrium continental status. Combined with other technological advances, this data-driven method may provide a path to solve Wegener’s puzzle of continental drift.

The theory of continental drift reconciled similar fossil plants and animals now found on widely separated continents. The southern part after Pangaea breaks (Gondwana) is shown here evidence of Wegener’s theory. (Image credit: United States Geological Survey)
The continental drift process of the data-driven simulations. Black arrow indicates the formation of the Antarctic. (Image credit: Gao et al., 2021)

The study was supported by the Department of Mathematics and Physics, Duke University.

CITATION: “Inbetweening auto-animation via Fokker-Planck dynamics and thresholding,” Yuan Gao, Guangzhen Jin & Jian-Guo Liu. Inverse Problems and Imaging, February, 2021, DOI: 10.3934/ipi.2021016. Online: http://www.aimsciences.org/article/doi/10.3934/ipi.2021016

Yuan Gao

Yuan Gao is the William W. Elliot Assistant Research Professor in the department of mathematics, Trinity College of Arts & Sciences.

Jian-Guo Liu is a Professor in the departments of mathematics and physics, Trinity College of Arts & Sciences.

Jian-Guo Liu

A Day of STEM for Girls

On any average weekday at Duke University, a walk through the Engineering Quad and down Science Drive would yield the vibrant and exciting sight of bleary-eyed, caffeine-dependent college students heading to labs or lectures, most definitely with Airpods stuck in their ears.

But on Saturday, February 22nd, a glance towards this side of campus would have shown you nearly 200 energetic and chatty female and female-identifying 4th to 6th graders from the Durham area. As part of Capstone, an event organized by Duke FEMMES, these students spent the day in a series of four hands-on STEM activities designed to give them exposure to different science, technology, engineering, and math disciplines.

Nina MacLeod, 10, gets grossed out when viewing fruit fly larvae through a microscope while her guide, Duke first-year Sweta Kafle, waits patiently. (Jared Lazarus)

FEMMES, which stands for Females Excelling More in Math, Engineering, and Science, is an organization comprised of Duke students with the aim of improving female participation in STEM subjects. Their focus starts young: FEMMES uses hands-on programming for young girls and hosts various events throughout the year, including after-school activities at nearby schools and summer camps. 

Capstone was a day of fun STEM exposure divided into four events stationed along Science Drive and E-Quad — two in the morning, and two in the afternoon, with a break for lunch. Students were separated into groups of around eight, and were led by two to three Duke undergraduates and a high school student. The day started bright and early at 8:45 A.M with keynote speaker Stacy Bilbo, Duke professor of Psychology and Neuroscience. 

Staci Bilbo

Bilbo explained that her work centers around microglial cells, a type of brain cell. A series of slides about her journey into a science career sparked awe, especially as she remarked that microglial cells are significant players in our immune system, but scientists used to know nearly nothing about them. Perhaps most impactful, however, was a particular slide depicting microglial cells as macrophages, because they literally eat cellular debris and dead neurons.

A cartoon depiction of this phenomenon generated a variety of reactions from the young audience, including but not limited to: “I’m NEVER being a doctor!”, “I wish I was a microglial cell!”, “Ew, why are brains so gross?”, and “I’m so glad I’m not a brain because that’s SO weird.”

Even in 2020, while fields like medicine and veterinary science see more women than men, only 20% of students that earn bachelor’s degrees in physical sciences, math, and engineering disciplines are female. What accounts for the dramatic lack of female participation in STEM disciplines? The reasons are nuanced and varied. For example, according to a 2010 research report by the American Association of University Women, girls tend to have more difficulty acquiring spatial thinking and reasoning skills – all because of the type of play young female children are more likely to engage in. 

Durham area students learned how to perform a blood pressure check during a FEMMES session taught by Duke EMS, an all-volunteer, student-run division of the police department and Duke Life Flight. Duke senior Kayla Corredera-Wells (center) put the blood pressure cuff on sophomore Pallavi Avasarala. (Jared Lazarus)

This creates a chicken-and-egg story: girls don’t enter STEM at the same rate as their male counterparts, and as a result, future generations of girls are discouraged from pursuing STEM because they don’t see as many accomplished, visibly female scientists to look up to. Spaces like Capstone which encourage hands-on activity are key to exposing girls to the same activities that their male counterparts engage in on a regular basis – and to exposing girls to a world of incredible science and discovery led by other females. 

After Bilbo’s talk, it was off to the activities, led by distinguished female professors at Duke — a nod to the importance of representation when encouraging female participation in science. For example, one of the computer science activities, led by Susan Rodger, taught girls how to use basic CS skills to create 3-D interactive animation.

An introduction to categorizing different minerals based on appearance was led by Emily Klein, while one of the medicine-centered activities involved Duke EMS imparting first aid skills onto the students. 

For one of the biology-themed activities, Nina Sherwood and Emily Ozdowski (dubbed “The Fly Ladies”) showed students fruit flies under a microscope. The activity clearly split the group: girls who stared in glee at unconscious flies, shrieking “It’s SO BIG, look at it!” and girls who exchanged disgusted looks, edging their swivel chairs as far as physically possible from the lab benches. Elizabeth Bucholz, a Biomedical Engineering professor, led one of the engineering activities, showing students how CT scans generate images using paper, a keychain light and a block (meant to represent the body). In math, meanwhile, Shira Viel used the activity of jump-roping to show how fractions can untangle the inevitable and ensuing snarls.

The day definitely wasn’t all science. During lunch in LSRC’s Love Auditorium, most groups spread out after scarfing down pizza and spent intense focus over learning (and recording) TikTok dances, and when walking down Science Drive under blue and sunny skies, conversations ranged from the sequins on someone’s Ugg boots to how to properly bathe one’s dog, to yelling erupting over someone confidently proclaiming that they were a die-hard Tar Heel.

Nina Sherwood, Associate Professor of Biology, showed Emma Zhang, 9, some fruit flies, which we study because they share 75% of their genes with humans. (Jared Lazarus)

A raffle at the end of the day for the chance to win Duke merchandise inspired many closed eyes and crossed fingers (“I want a waterbottle so bad, you have no idea!”) And as newfound friends said goodbye to each other and wistfully bonded over how much fun they had at the end of the day, one thing was clear: events like Capstone are crucial to instilling confidence and a love of STEM in girls. 

By Meghna Datta

The evolution of a tumor

The results of evolution are often awe-inspiring — from the long neck of the giraffe to the majestic colors of a peacock — but evolution does not always create structures of function and beauty.

In the case of cancer, the growth of a population of malignant cells from a single cell reflects a process of evolution too, but with much more harrowing results.

Johannes Reiter uses mathematical models to understand the evolution of cancer

Researchers like Johannes Reiter, PhD, of Stanford University’s Translational Cancer Evolution Laboratory, are examining the path of cancer from a single sell to many metastatic tumors. By using this perspective and simple mathematical models, Reiter interrogates the current practices in cancer treatment. He spoke at Duke’s mathematical biology seminar on Jan. 17.

 The evolutionary process of cancer begins with a single cell. At each division, a cell acquires a few mutations to its genetic code, most of which are inconsequential. However, if the mutations occur in certain genes called driver genes, the cell lineage can follow a different path of rapid growth. If these mutations can survive, cells continue to divide at a rate faster than normal, and the result is a tumor.

As cells divide, they acquire mutations that can drive abnormal growth and form tumors. Tumors and their metastases can consist of diverse cell populations, complicating treatment plans out patient outcomes. Image courtesy of Reiter Lab

With each additional division, the cell continues to acquire mutations. The result is that a single tumor can consist of a variety of unique cell populations; this diversity is called intratumoral heterogeneity (ITH). As tumors metastasize, or spread to other locations throughout the body, the possibility for diversity grows.

Intratumoral heterogeneity can exist within primary tumors, within metastases, or between metastases. Vogelstein et al., Science, 2013

Reiter describes three flavors of ITH. Intra-primary heterogeneity describes the diversity of cell types within the initial tumor. Intrametastatic heterogeneity describes the diversity of cell types within a single metastasis. Finally, inter-metastatic heterogeneity describes diversity between metastases from the same primary tumor.

For Reiter, inter-metastatic heterogeneity presents a particularly compelling problem. If treatment plans are made based on biopsy of the primary tumor but the metastases differ from each other and from the primary tumor, the efficacy of treatment will be greatly limited.

With this in mind, Reiter developed a mathematical model to predict whether a cell sample collected by biopsy of just the primary tumor would provide adequate information for treatment.

Using genetic sequence data from patients who had at least two untreated metastases and a primary tumor, Reiter found that metastases and primary tumors overwhelmingly share a single driver gene. Reiter said this confirmed that a biopsy of the primary tumor should be sufficient to plan targeted therapies, because the risk of missing driver genes that are functional in the metastases proved to be negligible.

 In his next endeavors as a new member of the Canary Center for Cancer Early Detection, Reiter plans to use his knack for mathematical modeling to tackle problems of identifying cancer while still in its most treatable stage.  

Post by undergraduate blogger Sarah Haurin

Post by Sarah Haurin

Leaving the Louvre: Duke Team Shows How to Get out Fast

Students finish among top 1% in 100-hour math modeling contest against 11,000 teams worldwide


Imagine trying to move the 26,000 tourists who visit the Louvre each day through the maze of galleries and out of harm’s way. One Duke team spent 100 straight hours doing just that, and took home a prize.

If you’ve ever visited the Louvre in Paris, you may have been too focused on snapping a selfie in front of the Mona Lisa to think about the nearest exit.

But one Duke team knows how to get out fast when it matters most, thanks to a computer simulation they developed for the Interdisciplinary Contest in Modeling, an international contest in which thousands of student teams participate each year.

Their results, published in the Journal of Undergraduate Mathematics and Its Applications, placed them in the top 1% against more than 11,000 teams worldwide.

With a record 10.2 million visitors flooding through its doors last year, the Louvre is one of the most popular museums in the world. Just walking through a single wing in one of its five floors can mean schlepping the equivalent of four and a half football fields.

For the contest, Duke undergraduates Vinit Ranjan, Junmo Ryang and Albert Xue had four days to figure out how long it would take to clear out the whole building if the museum really had to evacuate — if the fire alarm went off, for instance, or a bomb threat or a terror attack sent people pouring out of the building.

It might sound like a grim premise. But with a rise in terrorist activity in Europe in recent years, facilities are trying to plan ahead to get people to safety.

The team used a computer program called NetLogo to create a small simulated Louvre populated by 26,000 visitors, the average number of people to wander through the maze of galleries each day. They split each floor of the Louvre into five sections, and assigned people to follow the shortest path to the nearest exit unless directed otherwise.

Computer simulation of a mob of tourists as they rush to the nearest exit in a section of the Louvre.

Their model uses simple flow rates — the number of people that can “flow” through an exit per second — and average walking speeds to calculate evacuation times. It also lets users see what happens to evacuation times if some evacuees are disabled, or can’t push through the throngs and start to panic.

If their predictions are right, the team says it should be possible to clear everyone out in just over 24 minutes.

Their results show that the exit at the Passage Richelieu is critical to evacuation — if that exit is blocked, the main exit through the Pyramid would start to gridlock and evacuating would take a whopping 15 minutes longer.

The students also identified several narrow corridors and sharp turns in the museum’s ground floor that could contribute to traffic jams. Their analyses suggest that widening some of these bottlenecks, or redirecting people around them, or adding another exit door where evacuees start to pile up, could reduce the time it takes to evacuate by 15%.

For the contest, each team of three had to choose a problem, build a model to solve it, and write a 20-page paper describing their approach, all in less than 100 hours.

“It’s a slog fest,” Ranjan said. “In the final 48 hours I think I slept a total of 90 minutes.”

Duke professor emeritus David Kraines, who advised the team, says the students were the first Duke team in over 10 years to be ranked “outstanding,” one of only 19 out of the more than 11,200 competing teams to do so this year. The team was also awarded the Euler Award, which comes with a $9000 scholarship to be split among the team members.

Robin Smith – University Communications

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