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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

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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

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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

Kicking Off a Summer of Research With Data+

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On June 12, 2019

In Computers/Technology, Mathematics, Science Communication & Education, Statistics, Students, Visualization

If the May 28 kickoff meeting was any indication, it’s going to be a busy summer for the more than 80 students participating in Duke’s summer research program, Data+.

Offered through the Rhodes Information Initiative at Duke  (iiD), Data+ is a 10-week summer program with a focus on data-driven research. Participants come from varied backgrounds in terms of majors and experience. Project themes range  from health, public policy, energy and environment, and interdisciplinary inquiry.

“It’s like a language immersion camp, but for data science,” said Ariel Dawn, Rhodes iiD Events & Communication Specialist. “The kids are going to have to learn some of those [programming] languages like Java or Python to have their projects completed,” Dawn said.

Dawn, who previously worked for the Office of the Vice Provost for Research, arrived during the program’s humble beginnings in 2015. Data+ began in 2014 as a small summer project in Duke’s math department funded by a grant from the National Science Foundation. The following year the program grew to 40 students, and it has grown every year since.

Today, the program also collaborates with the Code+ and CS+ summer programs, with  more than 100 students participating. Sponsors have grown to include major corporations such as Exxonmobil, which will fund two Data+ projects on oil research within the Gulf of Mexico and the United Kingdom in 2019.

“It’s different than an internship, because an internship you’re kind of told what to do,” said Kathy Peterson, Rhodes iiD Business Manager. “This is where the students have to work through different things and make discoveries along the way,” Peterson said.

From late May to July, undergraduates work on a research project under the supervision of a graduate student or faculty advisor. This year, Data+ chose more than 80 eager students out of a pool of over 350 applicants. There are 27 projects being featured in the program.

Over the summer, students are given a crash course in data science, how to conduct their study and present their work in front of peers. Data+ prioritizes collaboration as students are split into teams while working in a communal environment.

“Data is collected on you every day in so many different ways, sometimes we can do a lot of interesting things with that,” Dawn said.  “You can collect all this information that’s really granular and relates to you as an individual, but in a large group it shows trends and what the big picture is.”

Data+ students also delve into real world issues. Since 2013, Duke professor Jonathan Mattingly has led a student-run investigation on gerrymandering in political redistricting plans through Data+ and Bass Connections. Their analysis became part of a 205-page Supreme Court ruling.

The program has also made strides to connect with the Durham community. In collaboration with local company DataWorks NC, students will examine Durham’s eviction data to help identify policy changes that could help residents stay in their homes.

“It [Data+] gives students an edge when they go look for a job,” Dawn said. “We hear from so many students who’ve gotten jobs, and [at] some point during their interview employers said, ‘Please tell us about your Data+ experience.’”

From finding better sustainable energy to examining story adaptations within books and films, the projects cover many topics.

A project entitled “Invisible Adaptations: From Hamlet to the Avengers,” blends algorithms with storytelling. Led by UNC-Chapel Hill grad student Grant Class, students will make comparisons between Shakespeare’s work and today’s “Avengers” franchise.

“It’s a much different vibe,” said computer science major Katherine Cottrell. “I feel during the school year there’s a lot of pressure and now we’re focusing on productivity which feels really good.”

Cottrell and her group are examining the responses to lakes affected by multiple stressors.

Data+ concludes with a final poster session on Friday, August 2, from 2 p.m. to 4 p.m. in the Gross Hall Energy Hub. Everyone in the Duke Community and beyond is invited to attend. Students will present their findings along with sister programs Code+ and the summer Computer Science Program.

Writing by Deja Finch (left)
Art by Maya O’Neal (right)

Biology by the Numbers

By

On December 18, 2018

In Behavior/Psychology, Biology, Guest Post, Mathematics

Michael C. Reed was trained as a pure mathematician, but from the start, he was, as he explained to me, a “closet physiologist.” He’s a professor of mathematics at Duke, but he’s always wondered how the body works.

Michael Reed in his office

Reed explains an example to me: women have elbows that are bent when their arms are straightened, but men do not. He rationalized his own explanation: women have wide hips and narrow shoulders; their bodies are designed so their arms don’t knock into their sides when they walk. (That basically ended up being the answer.)

Still, Reed never really explored his interest in physiology until he was 40 years old, when he realized that if he wanted to explore something, he should just do it. Why not? He had tenure by that point, so it didn’t really matter what his colleagues thought. He was interested in physiology, but was a mathematician. The obvious answer was mathematical biology.

Now he uses mathematics to find out how various physiological systems work.

In order to decide on a research project, he works with a biologist, Professor Fred Nijhout. They meet for two hours every day and work together. They have lots of projects, but they also just talk science sometimes. That’s how they get their ideas, mainly focusing on things in cell metabolism that have to do with important public health questions.

Reed has been investigating dopamine and serotonin metabolism in the brain, in a collaborative project with Nijhout and Dr. Janet Best, a mathematician at The Ohio State University.

Maybe better math is going to help us understand the human brain

As he explained to me, the brain isn’t like a computer; you don’t know how it works and there are a lot of systems in play. Serotonin is one of them. Low serotonin concentration is thought to be one of the causes of depression. There’s a biochemical network that synthesizes, packages, and transfers serotonin in the brain.

He told me that his work consists of making mathematical models for systems like this that consist of differential equations for concentrations of different chemicals. He then experiments with the system of differential equations to understand how the system works together. It’s not really something you can learn by having it explained to you, he told me. You have to learn through practice.

In a way, biology doesn’t seem like it would be the most compatible science, especially with math. But as Reed explained to me, “Math is easy because it’s very orderly and organized. If you work hard enough, you can understand it.” Biology, on the other hand, “is a mess.”

Everything in biology is linked to everything else in a system of connectedness that ends up all tangled together, and it can be hard to identify how something happens in the human body. But Reed applies math – an organized construct – to understand biological systems.

In the end, Reed does what he does because it’s how we — as human beings — work. He has no regrets about the choices he’s made at all.Mathematical biology seems to be his calling — he’s more interested in understanding how things work, and that’s what he does when he works.

Or rather, he doesn’t really work; because, as he told me,“try to find something to do that you really like, and are passionate about,because if you do, it won’t seem like work.” Reed doesn’t see coming into work as a struggle. He’s excited about it every single day and “it’s because you want to do it, it’s fun.”

Guest Post by Rachel Qu, NCSSM 2019

Artificial Intelligence Knows How You Feel

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On April 10, 2018

In Computers/Technology, Data, Engineering, Mathematics

Ever wondered how Siri works? Afraid that super smart robots might take over the world soon?

On April 3rd researchers from Duke, NCSU and UNC came together for Triangle Machine Learning Day to provoke everyone’s curiosities about the complex field that is Artificial Intelligence. A.I. is an overarching term for smart technologies, ranging from self-driving cars to targeted advertising. We can arrive at artificial intelligence through what’s known as “machine learning.” Instead of explicitly programming a machine with the basic capabilities we want it to have, we can make it so that its code is flexible and adapts based on information it’s presented with. Its knowledge grows as a result of training it. In other words, we’re teaching a computer to learn.

Matthew Philips is working with Kitware to get computers to “see,” also known as “machine vision.” By providing thousands and thousands of images, a computer with the right coding can learn to actually make sense of what an image is beyond different colored pixels.

Machine vision has numerous applications. An effective way to search satellite imagery for arbitrary objects could be huge in the advancement of space technology – a satellite could potentially identify obscure objects or potential lifeforms that stick out in those images. This is something we as humans can’t do ourselves just because of the sheer amount of data there is to go through. Similarly, we could teach a machine to identify cancerous or malignant cells in an image, thus giving us a quick diagnosis if someone is at risk of developing a disease.

The problem is, how do you teach a computer to see? Machines don’t easily understand things like similarity, depth or orientation — things that we as humans do automatically without even thinking about. That’s exactly the type of problem Kitware has been tackling.

One hugely successful piece of Artificial Intelligence you may be familiar with is IBM’s Watson. Labeled as “A.I. for professionals,” Watson was featured on Sixty Minutes and even played Jeopardy on live television. Watson has visual recognition capabilities, can work as a translator, and can even understand things like tone, personality or emotional state. And obviously it can answer crazy hard questions. What’s even cooler is that it doesn’t matter how you ask the question – Watson will know what you mean. Watson is basically Siri on steroids, and the world got a taste of its power after watching it smoke its competitors on Jeopardy. However, Watson is not to be thought of as a physical supercomputer. It is a collection of technologies that can be used in many different ways, depending on how you train it. This is what makes Watson so astounding – through machine learning, its knowledge can adapt to the context it’s being used in.

Source: CBS News.

IBM has been able to develop such a powerful tool thanks to data. Stacy Joines from IBM noted, “Data has transformed every industry, profession, and domain.” From our smart phones to fitness devices, data is being collected about us as we speak (see: digital footprint). While it’s definitely pretty scary, the point is that a lot of data is out there. The more data you feed Watson, the smarter it is. IBM has utilized this abundance of data combined with machine learning to produce some of the most sophisticated AI out there.

Sure, it’s a little creepy how much data is being collected on us. Sure, there are tons of movies and theories out there about how intelligent robots in the future will outsmart humans and take over. But A.I. isn’t a thing to be scared of. It’s a beautiful creation that surpasses all capabilities even the most advanced purely programmable model has. It’s joining the health care system to save lives, advising businesses and could potentially find a new inhabitable planet. What we choose to do with A.I. is entirely up to us.

Post by Will Sheehan

Will Sheehan

Jonathan Mattingly: Mathematics and Maps to Define Democracy

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On January 5, 2018

In Guest Post, Mathematics

Jonathan Mattingly is the chair of mathematics at Duke and an alumnus of the NC School of Science and Math

What began as an undergraduate project looking at how to create a “typical” map of congressional districts expanded to a national investigation for Duke mathematics chair Jonathan Mattingly. He was generous enough to speak to me about some of his recent work in mathematically investigating gerrymandering and the communication which followed between lawmakers and statisticians.

By strategically manipulating certain lines, it is possible to ensure a certain number of seats for one party even if that party does not win the majority vote. What “Team Gerrymandering” set out to do was to create an algorithm which would create the least biased map possible. The use of the term “fair” is complex in this instance, as politics and geography are very rarely simple enough to be split fairly.

An example of a mathematical model of precincts and districts.

In Wisconsin, the algorithm which “Team Gerrymandering” developed was used to prove that the voting districts were being disproportionately drawn in favor of the Republican votes, a trend which had was also been seen after the 2015 elections in North Carolina districts.

By strategically manipulating certain lines, it is possible to ensure a certain number of seats for one party even if that party does not win the majority vote. What “Team Gerrymandering” set out to do was to create an algorithm which would create the least biased map possible. The use of the term “fair” is complex in this instance, as politics and geography are very rarely simple enough to be split fairly.

The algorithm developed was then submitted as an brief amicus curae brief and used (it was used as a piece of appellate evidence) in the Wisconsin case Whitford vs. Bill. case. The mathematicians hoped to , in an attempt to prove that the districting of Wisconsin is an outlier in comparison to thousands of other mapping simulations run under their algorithm, which provide statistically sound data.

A problem such as this is a prime example of the bridge between the Humanities and STEM fields, which become increasingly separate as the level of expertise rises. as this truly bridges the humanities and STEM fields:, a solution has been found, but effectively communicating it was not as simple.

When asked about explaining and publishing this work in order to submit it as evidence, Mattingly admitted that it was, at times difficult, but it only further proved how important the effort is.

“It starts with a conversation. I’m willing to explain it, but you have to be willing to listen.”

A team full of lawyers looking to win a case is arguably a highly motivated audience, but this is not always the case. Mattingly, who is a 1988 graduate of the NC School of Science and Math which I attend, mentioned being at parties and hearing people state, “Oh, I’m no good at math, it’s just numbers and letters to me,” but he could never recount anyone saying “Oh, I don’t see the point in using language, or reading a dictionary.” These may seem like harmless comments, but a subconscious form of selective ignorance is still selective ignorance.

In light of the gerrymandering case, and “Team Gerrymandering’s” involvement in it, we are called to think again about the importance of fields we are not necessarily involved in, especially the STEM fields. What other patterns aren’t we noticing because we failed to look? Where else could we be improving if we were willing to listen? If we both don’t try, then we aren’t getting anywhere.”

The results of the Whitman vs Gill case are expected in June of 2018, and until then, the conversation must continue.

UPDATE: On Jan. 9, a federal court panel struck down North Carolina’s Congressional district maps on the grounds that they had been gerrymandered to favor Republicans. Mattingly commented.

Guest post by Paris Geolas, a senior at the North Carolina School of Science and Math

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