Dividing Your Neighbors: not to conquer, just to count

Hello!  I’m Joshua Wagner ’19, a chemistry and mathematics major at Gettysburg College.  Like any good mathematics major, I like to count things, and that’s good because I just spent the summer counting arithmetical structures on graphs with my research advisor, Dr. Glass.

Before we dive into my research topic, I would like to answer an interesting research question: “where is math research done?”  Well, all a researcher needs is a reliable laptop, a few pens (various colors help), a ream of paper (to scribble on before throwing away), some patience, chalk, and a blackboard.  So you can see that on days where the blackboard and chalk aren’t necessary, math research can be done anywhere.

Research can take place on a beautiful patio,

at a National Military Park,

or in Glatfelter Hall surrounded by professors and other students.  Where is the best place to conduct math research?  Gettysburg College, hands down.

Pivoting back to my summer research, to understand what it means to count arithmetical structures on graphs, we need understand two basic definitions.

First, what is a graph?  A graph is a group of nodes that are connected by edges. See the picture below:

Second, what is an arithmetical structure?  We can assign positive integers to each node on a graph, and if each node divides the sum of its neighbors and the greatest common divisor is one, we will call that assignment of integers an arithmetical structure. See the picture below:

There are much more complicated and rigorous ways to define an arithmetical structure using matrices, vectors, and complicated mathematical jargon, but this definition will suffice.

We already knew from a mathematician (Lorenzini) that any graph must have a finite number of valid arithmetical structures.  We also already have an algorithm for finding any arithmetical structures on a line of nodes, which we call a path, or a circle of nodes, which we call a cycle.

Now that you know what an arithmetical structure is, let’s say a few things about arithmetical structures on simple paths and cycles.  As we know, the first node on the end of a path must divide its neighbor.  We know that this second node must divide the third plus the first.  We can then see that the first node divides the third, and we can deduce that the first node must divide every other node evenly too.  (Try this with some scratch paper if you need convincing.)

Why does this matter?  Well, if the greatest common denominator of the values is 1, then the value of the first node must be 1 because it divides all the other nodes.  Similarly, we can see that if two nodes next to each other are equal, then those two nodes must evenly divide all the other nodes, so again we can see that if two neighboring nodes are equal, then they must be 1’s.

So, now we know that any path or cycle either has a local maximum, or is labeled with all ones.  In addition, we know that any local maximum must be the sum of its neighbors and that maximum can be removed to form another valid arithmetical structure.  In this example, 2 is a local maximum, so we can “smooth” the structure by removing it:

We can also do the inverse operation and add in a local maximum to create a more complex arithmetical structure:

From these facts we can make the lemma that any arithmetical structure on a path or cycle can be smoothed down to form a path or a cycle of all ones.  We can then also say that any arithmetical structure can be formed by adding in local maxima (like how we added the node with a 4 in the example above).

My research has been focused on counting how many arithmetical structures can be assigned to a given graph with more complex features.  Like, what would happen if two nodes were connected twice?

This complicates matters, as you can get a graph with a local maximum that is not the sum of its neighbors:

The number of “smooth structures,” or number of structures without a local maximum that is the sum of its neighbors is nontrivial to count.  It’s actually rather difficult to do and even harder to generalize.

How is math research performed?  I spent the first several weeks of the summer writing programs to find all of the arithmetical structures for smaller individual graphs.  From this data, we were able to distinguish patterns emerging.

Continuing through the summer, I spent less time programming, and more time writing proofs of why those patterns existed.  For instance, we noticed that one vertex next to a doubled edge seemed to always divide the sum of its neighbors twice (like 11 divides 2(9)+4 twice in the labeled graph above), so we proved that must happen.

We kept proving small things called lemmas until we were able to count all structures on more general graphs and form theorems.  For instance:

We were hoping that these theorems would piece together nicely and we could generalize our results to any path or cycle with a doubled edge.  We are still looking for a way to do this.

I presented our current findings in a 15 minute talk to professors and students from around the country on July 27th at MathFest, the Mathematical Association of America’s yearly meeting.  While in Chicago, we plan to learn some interesting math from leading mathematicians (and also have some deep dish pizza)!


Researching Magnetic Activity Cycles in Spotted Stars

By: Craig Cissel, Michael Preston, Ross Silver, Dr. Milingo

Our work this summer with Dr. Milingo has been filled with many exciting and educational experiences. I will break down our summer into three parts: data analysis, the observing run in Arizona, and community outreach.

Data analysis:

Our research goal was to find rotation periods and long-term activity cycle periods of selected stars in the cluster NGC 6811. We can determine this by using the image analysis program MIRA to perform photometry on our stars. We were looking for variations in brightness caused by spots on the star. The spots are an indication of magnetic activity in the star. We can use many years of data to see how the spots change and determine what the star’s activity cycle is.

NGC 6811

Figure 1: Our star cluster, NGC 6811.

In our day to day work, we mostly did image reduction and analysis using 5 years of images of NGC 6811 taken from the National Undergraduate Research Observatory (NURO). We extracted the difference in instrumental magnitude between our target star and a check star, whose brightness does not vary, and constructed light curves to determine the rotational periods. Then we put the data into a period finding routine to find our long-term activity cycle periods.

Observing at NURO:

NURO is located in Flagstaff, AZ. The NURO consortium consists of ~12 institutions and provides hands-on research opportunities specifically for undergraduates. The NURO telescope is the 0.8m which is part of Lowell Observatory. Our observing run was probably the highlight of our summer. We left on June 21st and came back on the 29th. When we landed in Phoenix at 10 am MST, it was a chilly 105º F. We then took the scenic route up to Flagstaff through Sedona. A few days later we went back to Sedona for lunch. It is one of the most beautiful places I have ever seen.



Figure 2: Two pictures of the scenery in Sedona, AZ.

            But this trip was not just for sight-seeing, we had work to do. We had 5 nights at the 0.8m telescope. Our work nights consisted of us showing up to the observatory around 6:45 pm, about an hour before sunset. We would open up the dome and take special images called flats and biases that we would later use to calibrate our NGC 6811 images. At the end of twilight, we would finish our focus routine and start taking images. We needed to refocus the telescope every hour due to the changes in temperature. While observing there is plenty of down time; we had many ways to entertain ourselves, including: binging Netflix, reading, watching anime, playing cards against humanity, or going outside to sit on a lounge chair and admire the night sky. We could see the sky so clearly because Flagstaff is the world’s first international dark sky city, http://www.flagstaffdarkskies.org/international-dark-sky-city/ . We continued until about 4 am because that’s when astronomical twilight started. Then we finished up with our shut down procedures. We would get home and go to sleep around 5 am. Then we could sleep until about 1 or 2 in the afternoon and relax or go out into town and explore before it was time to go to work again.


Figure 3: The top pictures shows the dome that holds the 31” telescope. The bottom picture is our lab group standing to the right of the telescope.

Our trip was filled with a lot of delicious food. We went to In N’ Out and Smashburger for burgers and milkshakes, Salsa Brava for tacos, and our celebratory dinner was at Texas Roadhouse for steaks. We hiked in Oak Creek Canyon which provided us with even more beautiful scenery. On our last full day of the trip, we went to see the Grand Canyon. We took a lot of pictures, but they could never fully capture the essence of the place.



Figure 4: The top shows our hike in Oak Creek Canyon. The bottom shows our lab group standing at the south rim of the Grand Canyon.

Community Outreach:

We spent part of our summer at the Gettysburg College Observatory, located on the northwest corner of campus. The 16” telescope is designed for use as a research-grade instrument for faculty and student projects, but the observatory is also used for public education and outreach. We held two open houses this summer: one during alumni weekend and one for the XSIG students. To prepare for an open house, we would come up with a list of objects that would be visible that night to show our guests and we studied the night sky so we could point out constellations and objects of interest. Unfortunately, there was about 80% cloud cover for the XSIG open house, which taught us to get used to clouds as we have no control over the weather. On cloudy nights, we bring our guests into the observatory and give them a tour of the classroom, the warm room, and the dome. We spent time learning about the history of the observatory and how the telescope and computers work so that we can teach the people how everything functions. These nights are always fun no matter what weather we have and we hope that we can do this more frequently during the school year.

We also created an astrominute for the community. An astrominute is a one-minute summary of what will be visible in the night sky that month in a certain part of the world and is aired on the radio. We wrote the script, recorded it, and layered it in Garageband. Thank you to Mark Drew, the advisor of the college radio station WZBT, who aired it on the radio and thanks to Ian Clarke, the director of the Hatter Planetarium, for assisting us with the music.

We started another project in the observatory that we hope to conclude this semester. Our 16” telescope does not have an eyepiece; the light goes directly into a CCD camera because it is used for research projects. It is difficult to pack a lot of people into our tiny warm room to show them what the telescope is pointing at, so we installed a large terminal screen out in the classroom that is connected to our 3” telescope that was previously used as an autoguider. An autoguider is a device on the telescope that tracks a bright star in the direction of our image and makes small adjustments to keep the star centered in the frame. The telescope then mimics these movements to prevent the image from drifting during a prolonged exposure. But our new CCD comes with a built in autoguider, so we can use the small 3” telescope to make it much easier for people to see what our telescope is looking at while in operation.

Get li

Figure 5: Our group going to Wine and Spirits to get beverages to entertain our alumni.

A Perfect Summer

Here in the Personality Lab, we’ve had the pleasure of exploring a variety of topics this summer, getting the opportunity to work with students on campus and collect data from people across the country through use of an online server.  While we touched on a broad span of topics, we took a particular interest in one: perfectionism.

For a majority of the summer, we spent our afternoons behind two closed doors and drawn curtains, and seated in front of a computer monitor.  Thankfully, though, we were never alone: on the other side of the doors, talking to us via Google Chat, was a student.  We got the chance to spend an hour talking to students about their views on perfectionism, what it meant to be perfect, and pressures which many of us feel to come across in a certain way.  Students answered our questions and talked about their own experiences with these pressures, whether they felt the need to hide the amount of effort they put into something or the anxiety which they felt, and perfectionism overall.

Perfectionism is a large topic, and while we had interest in perfectionism overall, we narrowed our sights onto a particular type: effortless perfectionism.  What is effortless perfectionism?  Let’s look at this example: a student has a large presentation to complete by the end of the semester.  They spend a significant amount of time trying to make the presentation appear perfect: good length, well-informed, well-delivered, aesthetically pleasing…whatever they can do to make the presentation ‘perfect,’ they do it.  Their friends may ask them if they want to hang out, and the student turns down the invitation to work on the presentation, but offers a different reason.  They might stay up late several nights to complete the presentation so as others will not know that they are working on it.  When they give their presentation to the class, they have a smooth delivery, since they had practiced often and knew the material well.  However, when asked by a classmate how much time the presentation had taken them to prepare, the student says that they did not spend a lot of time working on it.  Maybe they say that they only started looking at it a day or so ago, or that they feel they did poorly because they were ill-prepared.  No matter what the student says, they deny the idea that they had put in a lot of effort, and may overtly lie about their effort.

Effortless perfectionism takes traditional perfectionism to a different level: not only does everything the individual does have to appear perfect, but it has to appear to have happened naturally and effortlessly.  This has been a growing interest in the field in general, as students at high-pressure schools continue to struggle with mental disorders and demand for mental health treatment on campuses continues to escalate.

Despite this attention, no measure currently exists that targets this concept, a problem which we hope to fix through this study.  At present, effortless perfectionism has best been measured through scales assessing Hiding Effort (Flett, Nepon, Hewitt, Molnar, & Zhao, 2016), but this fails to capture the entirety of the construct.  It’s believed that this ‘hiding effort’ is related to effortless perfection, since both contribute to this image of achieving perfect work with seemingly minimal effort.  We used the anonymous interview process to ask students about their experiences with hiding their effort and anxiety, watching their peers hide their effort and anxiety, and to discuss the pressures they feel which influence why they hide and the type of image they feel they need to project.  Effortless perfectionism concerns hiding effort, but it also leads people to hide their anxieties.  The same student from earlier might become very anxious when they know they will have to speak in front of the class, for example, but they deny their anxieties surrounding this because it suggests that they are not perfect.  In order to appear naturally perfect, they must also be confident in themselves, and therefore must conceal any anxiety which they may feel.

Perfectionism is linked to several psychological disorders, and has been found to have group differences across age, gender, and socioeconomic status.  For these reasons, it is important to examine the finer details of perfectionism, especially a subtype such as effortless perfectionism, which is linked with higher rates of mental and emotional anguish.  Recently, universities and colleges across the United States have begun to form initiatives to address the issues arising from perfectionism, such as the ‘Failing Well’ movement at Smith College, to teach students to accept their failures and shortcomings in a healthy manner.  The Penn Faces movement at the University of Pennsylvania addresses similar concerns: teaching students at a high-stress institution that failure is part of life, and that resilience is important.

As fall semester rolls around, we’ll be thinking about more than just effortless perfection.    Self-compassion has been another topic of interest for the lab, and for good reason: manipulating state self-compassion has been found to have effects on a variety of measures, including pain tolerance.  In previous research conducted in this lab, it was found that a manipulation that increases state self-compassion could increase pain sensitivity in individuals with a history of self-harm, meaning they were able to withstand less pain after undergoing the manipulation (Gregory, Glazer, & Berenson, 2017). The concept of effortless perfectionism seems to be in contradiction with the principles of self-compassion.  The lab plans to examine what this relationship is, and how it can be manipulated to help those high in effortless perfection become more self-compassionate. We’re also looking to see whether a similar manipulation could affect the way an individual perceives stigma surrounding mental disorders in their community and ultimately increase their willingness to seek treatment.

Cool Beams

Hello all, I am Jonathan, and I, along with Edith, are doing research for Dr. Stephenson in the Physics department this summer. Professor Stephenson is part of the MoNA Collaboration, a group of faculty and students from primarily undergraduate institutions, as well as Michigan State where NSCL is located.   The Collaboration built the Modular Neutron Array (MoNA) to study neutron-rich nuclear reactions.

Our research area is nuclear prefragmentation, so looking at the way in which nuclei break apart when they hit each other. When two nuclei hit each other, they go through a two-step process.  First, the two nuclei tear each other apart.  Protons and neutrons are knocked out of both nuclei. These nuclei are, for a brief time, deformed and often have highly unbalanced ratios of neutrons and protons.  Since these new isotopes are unstable and deformed, they quickly decay by throwing out neutrons and gamma rays. How both steps really happen is not well understood since the time scale is so short (less than 0.0000000000000000000001s).  However, understanding this process, called nuclear prefragmentation, is important to creating rare isotope beams used at nuclear research facilities, like the National Superconducting Cyclotron Laboratory (NSCL), where we were last week.

The experiment was to create 9He nuclei in order to study how such a neutron-rich nuclei is put together.  We left for the experiment on Saturday July 8th, and a flight, an incredibly long wait for a rental car, and a drive later, we arrived at the NSCL 18273965954_7a5f463fc2_k

The NSCL is a huge facility that creates beams of rare isotopes for experiments. The NSCL does this by using two cyclotrons to accelerate nuclei to high speeds. This primary beam is then directed onto a target, which produces many different elements and isotopes. It then passes through a series of magnets and wedges of metal which select the correct secondary beam for the experiment. In our experiment, two different secondary beams were used, one of 11Be and one of 12B. The secondary beam is brought into the experimental vault, which is a huge room with tons of really fancy equipment, like the stuff below.file1-1The beam comes in, and strikes the target, and creates lots of new particles, including 9He. After this happens, the charged particles pass through a magnet which directs them into the charged particle detectors. The neutrons that are released are unaffected by the magnet, and continue on to the neutron detectors called MoNA and LISA (Large multi-Institution Scintillator Array). While we were there, we learned a lot, and survived our first overnight experimental shift, but none of it would have been possible without the incredible people. So many people took the time to explain to us what they were doing, why it needed to be done, and let us help them in whatever way possible. Our last day at NSCL, we had the opportunity to go on a tour of the new facility, FRIB (Facility for Rare Isotope Beams) which is being built. We met in the FRIB office trailer, and donned our stylish hard hats, protective eyewear, and safety vests, and went with the rest of the MoNA collaborators into the new facility.  file6

The FRIB facility is the new accelerator which is being built at MSU. The accelerator will be located in a gigantic underground room, which is surrounded on all sides by between four and fourteen feet of solid concrete. The room is more than three hundred feet long, fifty feet wide, and fifteen feet high, and will have between 350 and 400 miles of cables in it. We got to tour the entire facility, except the target room, which is currently closed to the public. The FRIB facility, scheduled to be finished in 2022, will be amazing, and I left with a renewed excitement for physics.


Salmonella: Beyond chickens and eggs….



Salmonella is the number one foodborne bacterial pathogen in the US.  The Shariat lab(aka the CRISPR Crew) is developing a new technique that allows us to survey the diversity of this bacterium within a single sample.  While we always think of chickens and eggs, it is known that Salmonella can also be found in water.  For the last several months, we have been working on a project to investigate Salmonella diversity in our local rivers and creeks.  What better place to start this investigation than in our very own watershed!  Since all Gettysburgians know that campus is drastically different during        each season,our team co


Map of the creeks where we sampled

llected water samples in November and April so we could compare how those seasonal changes affected bacterial diversity.  We selected 60 different sites across three different creeks – Marsh Creek, Willoughby Run, and Rock Creek.



While the rest of campus was enjoying SpringFest festivities, we headed out into the community sporting our thigh high waders, ready for a day of sample collection.  Some of our locations were easy access, but we had a few exciting encounters, including meeting some snakes as they seemingly fell from the sky (or maybe just a low hanging branch) into the river next to us, plus getting stuck in some nasty mud on one river bank!  We also got drenched in a mid-day deluge.  All in the name of science!


Sunrise water collection in Marsh Creek; definitely warmer than the November collection!

In lab this summer, our main focus was processing these samples we collected to determine whether we could find any Salmonella (spoiler: don’t go swimming in our creeks, Salmonella is everywhere!). After we collected water, we had to extract DNA from the bacteria and do PCR to replicate the isolated DNA (we need a lot of DNA to do our experiments). PCR uses a lot of enzymes and other stuff that shouldn’t be in our final samples, so we had to remove these things using a REALLY POWERFUL MAGNET that is super cool and makes DNA stick to it, so you can remove everything else quickly and easily without losing the DNA.  We’re currently sequencing our samples to identify exactly which types of Salmonella are present.



CRISPR Crew Cares Day

During our water collection, we noticed that the banks of some of our local creeks have a LOT of trash, so we decided to do a river clean up for our second annual CRISPR Crew Cares day.  On a drizzly morning, we headed out to the historic Sachs Covered Bridge (if you haven’t visited this yet, you totally should!) that spans Marsh Creek. We spent the morning collecting trash on the bridge (which may or may not be inhabited by ghosts) and along the creek. Notable finds include computer parts, travel size liquor bottles, yards of fishing wire, and a handful of batteries.


The CRISPR-Crew loves science and service!

Bacteria and a famous battle…

We recently had the opportunity to meet with Dr. Eric Brown, Director of the Division of Microbiology in the Office of Regulatory Sciences at the United States Food and Drug Administration, and members of his awesome research team.  Their research program is focused on food safety – keeping pathogenic bacteria such as Salmonella out of our food chain.  The research we do in the Shariat Lab focuses on effectively subtyping and identifying different kinds of Salmonella from different sources, such as the creeks surrounding campus. We had the


These are just some ‘surprising’ foods responsible for Salmonella outbreaks in recent years


opportunity to share our findings with the FDA research team through student presentations and to also listen to some of their exciting research programs and discoveries they’ve made.  We loved the opportunity to have such advanced conversations with experts in the field and it was cool to learn about federal research programs.

To top off an awesome day, it turns out that Dr. Brown is not only a scientist, but apparently knows more about Civil War history than the majority of Gettysburg College students!  After a morning of science, the whole group headed over to the battlefield where he gave us an incredible tour of two major sites of the Battle of Gettysburg (Little Round Top and Pickett’s Charge). Other tourists even joined our group thinking that Dr. Brown was a professional tour guide!  All in all, we had a lot of fun and it was an amazing opportunity.


A bunch of Salmonella experts learning about the civil war


The Effects of Treadmill Training on Solid Meal Gastric Emptying

My name is Theresa Blickenstaff (’20), and this summer I have been privileged to work one-on-one with Dr. Emily Besecker in the Health Sciences department here at Gettysburg College. Our research is essentially looking at whether a long-term, moderate-intensity exercise program causes food to move from the stomach and into the small intestine at a different rate as compared to a control group that is not exercised. That is, when you exercise chronically at a moderate-intensity, is your body able to more efficiently move ingested materials through the digestive system? Current scientific literature is divided on this subject, and there is not a definitive answer to this question because of the variables present with exercise (for example, type, duration, and intensity of exercise) and the foodstuffs (for example, solid as opposed to liquid meals, and the nutritional composition of the food). With the results of our study, we hope to reach a more conclusive and satisfying answer to this question.

Pic 1Now, you may be asking yourselves how we are going to collect our data. Have we bribed some poor souls into coming with us each day to the Jaeger fitness center and jogging on the treadmills while we stand by with our pens and clipboards, encouraging the runners with the promise of a nice meal afterwards? Well, no. What we are doing is much more complicated.


Our experimental model is actually the rat—the male Wistar rat, to be more precise. These rats are albino and are widely used for scientific and biological research. On account of the generous funding provided by Gettysburg College, we were able to obtain sixteen rats for use in this study, meaning that we have a large enough sample size to reach statistical significance in our results, should there be differences between the exercise and the control groups. Based on their compliance to the exercise, the rats were divided into the exercise and control groups at the beginning of the study, with eight rats in each group. Now, how exactly are we getting these cute, energetic little guys to exercise, you might ask? Well, we are using a treadmill set up in one of our labs. Just like the treadmills you are used to, this treadmill has a belt that moves at a speed that you can program. Unlike the treadmills you are probably used to, however, this treadmill has multiple lanes allowing 3-4 rats to run simultaneously (even rats enjoy a little friendly competition!).

The reason we are using a treadmill and not, say, bicycles, is that treadmills cause the rats to run or jog. This type of movement is somewhat jarring to the body, and it can cause the internal organs—including the stomach—to jostle around a bit more than any other type of exercise. As we want to see how exercise can influence the functional properties of the stomach, this type of exercise is ideal for our research.

One of my primary jobs over the course of this summer has been to exercise the rats. This is easier said than done, as I learned very quickly. See, male rats are tricky. When they are not on the treadmill, they are energetic and feisty and a general joy to be around. When they are placed on the unmoving treadmill even, they are still happy and curious. Once the treadmill belt starts moving, however, many of the rats take on whole new personalities, some of them even aging before my eyes into elderly men who just cannot—that is, will not—move forward. At times like these it is necessary for me to encourage the rats, as our study will essentially be pointless if our exercise group rats do not exercise. The tools that I have used to encourage the rats include soft brushes, flimsy cardboard, pressurized air, and delicious pancake treats. Sometimes what works for one rat will not work for another, so some creativity is definitely involved. In addition, the rats do tend to become used to certain kinds of stimulation if exposed to them for long periods of time, so I do rotate the encouragement-tools that I use. Sometimes it even just depends on the day—what works on one day may not work the next day. Generally, however, I have been able to train the rats to the point where many of them will exercise with minimal encouragement.

Pic 2Each day of the week the rats are exercised for one hour at a moderate pace akin to a jog/light run. They are allowed to take short breaks on the non-moving grid at the back of the treadmill as needed. On Saturday and Sunday, the rats rest. This rest is optimal for muscle recovery but sub-optimal for compliance when working with male rats. Nevertheless, the exercise training is an eight-week period consistent with non-acute exercise programs described in the scientific literature.



Enough about running, let’s discuss breathalyzers…To collect the data on the rate at which food is passed from the stomach into the small intestine, a process known as gastric emptying, we are using the 13carbon-octanoic acid breath test. This test is used three times over the course of the eight weeks of treadmill training: once at the beginning to obtain a baseline reading for each rat, once in the middle of the eight weeks, and once at the end of the eight weeks. For this experiment, the rats ingest a small portion of pancake labeled with 13C-octanoic acid. The pancake is used because we are trying to simulate a standard solid meal; that is, one that is not too fatty and does not introduce unnecessary difficulties to the stomach’s natural process of digestion.

Once ingested, the carbon-13-octanoic acid is broken down in the stomach and passed into the small intestine. It is absorbed into the bloodstream and then travels to the liver. Here, it is oxidized and metabolized to carbon-13 CO2, which then is taken to the lungs by the bloodstream and exhaled from the lungs. The rats are placed into individual chambers for approximately 7 hours as the infrared isotope analyzer measures the ratio of 13CO2:12CO2 of the rat’s exhaled breath; therefore, the breathalyzer test is a measure of gastric emptying rate. The faster the 13CO2 is detected, the faster the stomach is digesting and emptying its contents.

Pic 3In addition to these gastric emptying data points, I have also been measuring the body weights and food intake weights of all sixteen rats each day. These data are being used to calculate the mean energy intake (MEI) for each of the rats. This data collection will provide insights into how the body weights of the rats are changing over time, how the amount of food they are eating is changing, and how the average number of calories they are taking in relative to their body mass is changing over time. This information is of interest specifically in regards to the differences between the exercise and control groups and in ensuring that nutritional demands are being met properly.

Now that you know the basics of our summer research project, one question that is likely still on your mind is how this research is relevant. Why does the speed at which food moves through the stomach matter? It actually matters a great deal. The speed of movement influences the rate at which nutrients can be absorbed into the body and used as an energy source. For individuals living with gastric dysmotility and other disorders that cause their stomach or gastrointestinal tract to not function efficiently, the rate at which their body can access the nutrients they ingest is slowed, causing a whole host of problems of its own. The results of this study are likely to provide insight into creating treatments for senior citizens and other individuals living with gastrointestinal disorders. Rather than having to take medicine for their condition, individuals with delayed gastric emptying could potentially partake in a moderate-intensity exercise program to help treat their condition. In a world where exercise is continuing to be shown as immensely important and beneficial to the body, such a positive result to our study would be yet another jewel in exercise’s crown as the natural medicine of the body.

What Fish Do in Shadows?

Collective behavior and self-organization are very common in living systems and exhibited across many different scales including cells, colonies of insects, schools of fish, and crowds of people. These systems, while familiar, are not well understood. Collective systems contain a large number of interacting components that exhibit complex dynamics. In nature, individuals benefit from the advantages of group living. It is expected that group behavior in animals often arises from evolutionary necessity. However, not much is known about the mechanics of these systems in nature due to their complexity. How do groups of animals work together to navigate complex environments? How does information travel throughout a group? We use computers and schools of fish to gain a more in depth knowledge of how and why collective groups organize themselves in such interesting ways.

Collecting Quantitative Data (Julia Giannini ‘18, Aawaz Pokhrel ‘19, Nicole Linard ‘20)


To investigate how individual interactions give rise to collective states, we use the apparatus above to observe the response of experimental schools to visual stimuli. This summer, we worked with two different species of schooling fish: Rummy-nose Tetra (left) and Golden Shiners (right). Both of these fish exhibit negative phototaxia, that is, they avoid bright regions in their environment. Therefore, we can project light gradients onto the tank and examine how they respond to both social and environmental cues.  Using infrared lighting and high speed cameras, we record videos and use lots of machine vision techniques to extract individual trajectories. This information gives us insight into the state of the group over time and how it relates to individual movement. By using both Tetras and Shiners, we compare the behaviors of different species under the same stimuli.

Here is a video of Golden Shiners tracking a noisy dark blob – we compare experimental results such as these with those in simulations to test theoretical models for collective behavior.


Simulation of Collective Behavior (Aawaz Pokhrel ‘19)

So, how do fish find the darkest (safest) spot in their environment?  Can they see the gradient (slope) of light and follow it to the safest place?  Or do they use emergent sensing (group level sense)?  We explore the answer to this with both simulations and experiments.

In the simulation, we use the Couzin model which has three different zones which dictates the movement of the fish on basis of the positions of neighbour fish in these zones. These three zones are zones of repulsion, orientation and attraction. One of the assumption of that we have in this model simulation  is that fish are not able to sense the gradient or the change of light field in any direction.

Here is a short  video of our simulation fish trying to follow the dark spot.

We amend this model by adding in a gradient sensing term which competes with the social-only Couzin model.  By turning the “knob” of this weight (how well the fish can sense the gradient), we investigate how it affects the performance of the fish in finding the darkest spot.
We see that the more amount of information they have about the gradient, the less they are able to track the dark spot. Following graph shows that for a given number of fish, their ability to track the dark spot decreases Ψ as the amount of information about the gradient increases.


Use of neural network in Collective Behavior (Nicole Wang ‘19)

Another difficulty with understanding and predicting collective behavior is that the interactions are not known.  And of course, it’s not possible to ask the fish how they are interacting.  So we must build models and compare with experimental data.  However, each model we build has assumptions about how the fish are interacting.  A widely used model the Couzin model uses zones (repulsion, alignment, attraction) to predict the behavior of individuals.  We are using neural networks to train a computer to learn how the fish are interacting.


As shown in above figure, the neural network uses an input layer which in our case is the visual field of nearby fish.  This input layer is connected with several hidden layers and finally a single output neuron telling the fish which direction to turn.  In our neural network, we use both convolutional and fully connected layers, which of course means — lots of linear algebra.  We test this approach on a simulation of a fish school (using the Couzin model) so that we can directly compare the output generated by the Neural Network with the known model.  Finally, we apply the NN-approach to our experimental data.  We’re still working out some of the details, but the NN seems to be working very well !!!