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Category: Mathematics Page 2 of 8

Undergraduate Researchers William He and Annie Wang Dig Deeper into Hypergraphs

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On November 22, 2021

In Mathematics, Students

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!

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On October 21, 2021

In Faculty, Mathematics, Science Communication & Education

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

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On October 13, 2021

In Art, Artificial Intelligence, Data, Mathematics, Statistics, Students

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

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On September 17, 2021

In Behavior/Psychology, Biology, Biomedical Engineering, Chemistry, Climate/Global Change, Engineering, Environment/Sustainability, Mathematics, Medicine, Physics, Science Communication & Education

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

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On April 14, 2021

In Computers/Technology, Data, Faculty, Guest Post, Mathematics, Physics, Visualization

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

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On March 10, 2020

In Biology, Computers/Technology, Engineering, Mathematics, Science Communication & Education, Students

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

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On January 23, 2020

In Biology, Cancer, Genetics/Genomics, Lecture, Mathematics, Medicine

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. Intra–metastatic 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

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On September 12, 2019

In Art, Behavior/Psychology, Computers/Technology, Mathematics, Students

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

Science in haiku: // Interdisciplinary // Student poetry

By

On August 9, 2019

In Data, Engineering, Mathematics, Statistics, Students

On Friday, August 2, ten weeks of research by Data+ and Code+ students wrapped up with a poster session in Gross Hall where they flaunted their newly created posters, websites and apps. But they weren’t expecting to flaunt their poetry skills, too! 

Data+ is one of the Rhodes Information Initiative programs at Duke. This summer, 83 students addressed 27 projects addressing issues in health, public policy, environment and energy, history, culture, and more. The Duke Research Blog thought we ought to test these interdisciplinary students’ mettle with a challenge: Transforming research into haiku.

Which haiku is your
favorite? See all of their
finished work below!

Eric Zhang (group members Xiaoqiao Xing and Micalyn Struble not pictured) in “Neuroscience in the Courtroom”
Maria Henriquez and Jake Sumner on “Using Machine Learning to Predict Lower Extremity Musculoskeletal Injury Risk for Student Athletes”
Samantha Miezio, Ellis Ackerman, and Rodrigo Aruajo in “Durham Evictions: A snapshot of costs, locations, and impacts”
Nikhil Kaul, Elise Xia, and Mikaela Johnson on “Invisible Adaptations”
Karen Jin, Katherine Cottrell, and Vincent Wang in “Data-driven approaches to illuminate the responses of lakes to multiple stressors”.

By Vanessa Moss

Overdiagnosis and the Future of Cancer Medicine

By

On June 17, 2019

In Biology, Cancer, Data, Faculty, Genetics/Genomics, Mathematics, Medicine

For many years, the standard strategy for fighting against cancer has been to find it early with screening when the person is still healthy, then hit it with a merciless treatment regimen to make it go away.

But not all tumors will become life-threatening cancers. Many, in fact, would have caused no issues for the rest of the patients’ lives had they not been found by screening. These cases belong to the category of overdiagnosis, one of the chief complaints against population-level screening programs.

Scientists are reconsidering the way to treat tumors because the traditional hit-it-hard approach has often caused the cancer to seemingly go away, only to have a few cells survive and the entire tumor roar back later with resistance to previously effective medicine.

Dr. Marc Ryser, the professor who gave this meaty talk

In his May 23 talk to Duke Population Health, “Cancer Overdiagnosis: A Discourse on Population Health, Biologic Mechanism and Statistics,” Marc Ryser, an assistant professor at Duke’s Departments of Population Health Sciences and Mathematics, walked us through how parallel developments across different disciplines have been reshaping our cancer battle plan. He said the effort to understand the true prevalence of overdiagnosis is a point of focus in this shift.

Past to Future: the changing cancer battle plan
Credit: Marc Ryser, edit: Brian Du

Ryser started with the longstanding biological theory behind how tumors develop. Under the theory of clonal sweeps, a relatively linear progression of successive key mutations sweeps through the tumor, giving it increasing versatility until it is clinically diagnosed by a doctor as cancer.

Clonal sweeps model, each shade is a new clone that introduces a mutation credit: Sievers et al. 2016

With this as the underpinning model, the battle plan of screen early, treat hard (point A) makes sense because it would be better to break the chain of progression early rather than later when the disease is more developed and much more aggressive. So employing screening extensively across the population for the various types of cancer is the sure choice, right?

But the data at the population level for many different categories of cancers doesn’t support this view (point B). Excluding the cases of cervical cancer and colorectal cancer, which have benefited greatly from screening interventions, the incidence of advanced cases of breast cancer and other cancers have stayed at similar levels or actually continued to increase during the years of screening interventions. This has raised the question of when screening is truly the best option.

Scientists are thinking now in terms of a “benefit-harm balance” when mass-screening public health interventions are carried out. Overdiagnosis would pile up on the harms side, because it introduces unnecessary procedures that are associated with adverse effects.

Thinking this way would be a major adjustment, and it has brought with it major confusion.

Paralleling this recent development on the population level, new biological understanding of how tumors develop has also introduced confusion. Scientists have discovered that tumors are more heterogeneous than the clonal sweeps model would make it appear. Within one tumor, there may be many different subpopulations of cancer cells, of varying characteristics and dangerousness, competing and coexisting.

Additional research has since suggested a more complex, evolutionary and ecological based model known as the Big Bang-mutual evolution model. Instead of the “stepwise progression from normal to increasingly malignant cells with the acquisition of successive driver mutations, some cancers appear to evolve more like a Big Bang, where the malignant ability is already concentrated in the founder cell,” Ryser said.

As the first cell starts to replicate, its descendants evolve in parallel into different subpopulations expressing different characteristics. While more research has been published in favor of this model, some scientists remain skeptical.

Ryser’s research contributes to this ongoing discussion. In comparing the patterns by which mutations are present or absent in cancerous and benign tumors, he obtained results favoring the Big Bang-mutual evolution model. Rather than seeing a neat region of mutation within the tumor, which would align with the clonal sweeps model, he saw mutations dispersed throughout the tumor, like the spreading of newborn stars in the wake of the Big Bang.

How to think about mutations within a tumor
credit: NASA

The more-complicated Big Bang-mutual evolution model justifies an increasingly nuanced approach to cancer treatment that has been developing in the past few years. Known as precision medicine (point C), its goal is to provide the best treatment available to a person based on their unique set of characteristics: genetics, lifestyle, and environment. As cancer medicine evolves with this new paradigm, when to screen will remain a key question, as will the benefit-harm balance.

There’s another problem, though: Overdiagnosis is incredibly hard to quantify. In fact, it’s by nature not possible to directly measure it. That’s where another area of Ryser’s research seeks to find the answers. He is working to accurately model overdiagnosis to estimate its extent and impact.

Going forward, his research goal is to try to understand how to bring together different scales to best understand overdiagnosis. Considering it in the context of the multiscale developments he mentioned in his talk may be the key to better understand it.

Post by Brian Du

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