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Trident Scholar Program
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Trident Scholar Abstracts 2022

Matthew J. Fox
Midshipman First Class
United States Navy

Structural and Magnetic Properties of Iron-Palladium and Iron-Nickel Nanoparticle Biocomposites

Biocomposites containing magnetic nanoparticles have the potential to combine the unique, tunable properties of nanoparticles with the strong mechanical and environmentally sustainable properties of natural fibers like cellulose. Materials derived from biocomposites can be used for a broad variety of civilian and military applications including electromagnetic shielding, thermoelectrics, functional textiles, and water filtration. Many recent studies have focused on magnetic nanoparticles because of the unique properties that emerge when the size of particle reaches the nanoscale. Recently, a method to synthesize Fe-Pd nanoparticles in cellulose has been developed. This study presents a detailed investigation on how magnetic properties of Fe-Pd nanoparticles are affected by increasing the metal load at a fixed atomic composition. An analysis of their magnetic response in static and dynamic magnetic fields indicates a polydisperse ensemble of nanoparticles with up to four distributions of blocking temperatures. Each distribution of blocking temperatures corresponds to a distinct group of particles. Peak dependence on frequency, field, and load was analyzed for each group of nanoparticles. In addition to the Fe-Pd studies, novel Fe-Ni nanoparticle biocomposites are presented for the first time. A unique energetic event during the N2 (nitrogen) reduction at 120 °C has been observed in samples with < 2 at. % Fe. A similar event is seen at higher Fe loads when the N2 reduction is performed at higher temperatures. During this event, the cellulose matrix is degraded, an ensemble of Ni-Fe magnetic nanoparticles is formed with different distributions of blocking temperatures, and the materials appear to store hydride. For samples for which no energetic event occurs, limited nanoparticle growth and weak magnetic properties are observed. The introduction of Fe into the Ni matrix appears to cause increased magnetic disorder. Both systems have been developed and characterized with the goal of creating magnetically active nanoparticle biocomposites for potential applications in electromagnetic shielding.

FACULTY ADVISORS
Professor Elena Cimpoiasu
Physics Department

CDR David Durkin, USN
Chemistry Department


Kade M. Heckel
Midshipman First Class
United States Navy

Competitively Learned Attention Mechanism Prototypes for Network Intrusion Detection

Maintaining secure computer networks and information systems are vital to the administrative functions and operations carried out by the Department of Defense (DOD). However, the diverse ecosystem of weapons platforms from various defense contractors and large enterprise networks results in many data formats, complicating the analysis process for Cyber Protection Teams conducting Defensive Cyber Operations (DCO). Additionally, identifying an adversary’s actions among the noise of everyday network behavior poses a significant challenge due to the subtle methods employed to disguise their actions.

With advances in computer architecture in the last decade enabling an explosion in deep learning, neural networks with millions or billions of parameters have emerged as powerful tools in machine learning. However, previous work on applying neural networks to intrusion detection has focused on recurrent and convolutional neural networks but has yet to explore attention-mechanism-based architectures inspired by the Transformer in Vaswani et al. (2017). These attention-based models contain layers that produce rich contextualized representations through learning pairwise interactions within data sequences, enabling tremendous advances in computer vision and natural language processing over the last five years.

This research investigated the performance of attention-based neural network architectures compared to traditional models on the University of New Brunswick’s CSE-CIC-IDS2018 dataset. Evaluating models on precision, recall, and the Area Under the Receiver Operating Characteristic Curve (AUROC), results show that models leveraging attention mechanisms performed demonstrably better than a tuned feed-forward network on the infiltration attack class. Additionally, this work explores a novel attention mechanism for improving the efficiency of neural network attention mechanisms by learning a compressed representation of the data through competitively-learned memory prototypes, showing competitive performance against an alternative efficient attention architecture that utilizes gradient descent.

FACULTY ADVISOR
Associate Professor Frederick Crabbe
Computer Science Department


Jonathan J. Huang
Midshipman First Class
United States Navy

Electrochemical and Spectroscopic Investigations of Bismuth Ions with Sulfur-Containing Biomolecules

Bismuth complexes involving amino acids provide a model system for probing physiological interactions between bismuth and the abundant thiol-containing proteins in the digestive system, whose direct study would be prohibitively complex. Such interactions may prove beneficial in the improvement of pharmaceutical agents, especially bismuth-containing metallodrugs. Interactions of bismuth pharmaceuticals including bismuth subnitrate (bismuth(III) nitrate), bismuth subsalicylate (bismuth(III) salicylate), and bismuth(III) citrate with sulfur containing biomolecules such as L-cysteine and L-glutathione were investigated by cyclic voltammetry and UV-Vis spectroscopy in different pH environments to characterize the formation of complexes between the bismuth(III) ion and the thiol-containing ligands. Experiments were carried out at pH 1 and 3 to mimic the acidity of stomach contents and pH 7.4, to mimic that of general physiological conditions, in order to identify pH effects on complex formation. Cyclic voltammetry was employed to identify reduction potential shifts that accompany complex formation. Similarly, UV-Vis spectroscopy was used to monitor complexation at a characteristic peak that forms near the 340 nm wavelength. Analysis showed that indeed the pH, the type of thiol-containing compound, and the starting bismuth pharmaceutical had an effect on the complex formation. More acidic conditions lessen the interaction of L-cysteine with bismuth(III) due to protonation effects on the thiol-containing compound.

FACULTY ADVISORS
Professor Graham Cheek
Chemistry Department

Professor Jamie Schlessman
Chemistry Department


Ψ William A. Jarrett
Midshipman First Class
United States Navy

Machine Learning-based Design of Structured Laser Light for Improved Data Transfer Rate in Underwater Wireless Communication

To meet the demand for high data transfer rate underwater wireless communication systems, a system using Laguerre-Gaussian (LG) beams of structured light and deep convolutional neural networks (CNNs), is proposed [1]. In this system, the structured beams of light are encoded through superposition to carry information, possible due to the orthogonality of the LG beam, with each combination resulting in a distinct image. This creates an alphabet of 2^N, images, where N is the number of basis beams and bits encoded per message. Previous work has evaluated network performance using alphabets ranging from 16 beams to 32 beams. For this investigation, a novel methodology for optimizing network alphabet design is proposed, and 256 and 1024-beam alphabets are designed for optimal classification accuracy through optical turbulence using a CNN. The alphabets were evaluated in the simulated and experimental environments. For the simulated environment, the beams were propagated using the split-step method through random phase screens drawn from the Nikishov spectrum for oceanic turbulence. In the experimental environment, the beams were propagated over ~2.5 meters through optically turbulent water with strong turbulent fluctuations. This study is novel in its use of the scintillation of a Gaussian beam to estimate the strength of the turbulence in real-time. In the simulated environment, we report 100% classification accuracy for the 256-beam alphabet, indicating the CNN’s ability to learn weak fluctuations. Under experimental conditions, we report over 97% accuracy for 256-beam alphabets, and over 90% accuracy for the 1024-beam alphabet. We find that our CNN is capable of classifying the alphabet symbols provided sufficient training data is available and representative of the testing data. A greater challenge arises when the network is tested on images with altered beam alignment.

FACULTY ADVISORS
Professor Svetlana Avramov-Zamurovic
Weapons, Robotics, and Control Engineering Department

Professor Joel Esposito
Weapons, Robotics, and Control Engineering Department

Kyle G. Jung
Midshipman First Class
United States Navy
 
An Analytical and Computational Study of the Paraxial Wave Equation with Applications to Laser Beam Propagation
 

In this project, we approximate solutions to the Paraxial Wave Equation by posing an initial boundary value problem (IBVP). The Paraxial Wave Equation is a model of laser beam propagation. A variable refractive index term is introduced within this partial differential equation to account for a nonhomogeneous medium. We apply Spectral methods to approximate the transverse Laplacian operator and an adaptive Runge-Kutta method using MATLAB’s ordinary differential equation solvers to propagate the beam forward in space. Three Spectral methods are considered: a Fourier Galerkin method, a Fourier collocation method, and a Chebyshev collocation method. These methods are verified in two ways: (1) by comparing the numerical IBVP solution to the exact solution in unbounded space for a Gaussian beam propagating in homogeneous media and (2) by applying the method of manufactured solutions. We apply a Fourier collocation method to model laser beam propagation through a nonhomogeneous medium.

FACULTY ADVISORS
Professor Reza Malek-Madani
Mathematics Department

Professor Svetlana Avramov-Zamurovic
Weapons, Robotics, and Control Engineering Department

Samuel P. Laney
Midshipman First Class
United States Navy

Participant and Channel Privacy in End-to-End Encrypted VoIP Teleconferencing

Voice over Internet Protocol (VoIP) chat services such as Discord allow organizations, teams, and friends to easily connect to one another with voice teleconferencing and text chat. However, most VoIP traffic is either unencrypted or encrypted only in transit, meaning that a compromised or over-curious server can analyze and listen to any and all traffic sent through it. Some schemes currently exist that improve security by implementing full end-to-end encryption, meaning that the server cannot interpret the contents of a message, but these schemes still reveal conversation metadata such as who is in a channel and who is talking at any given time.

Our research implements a teleconferencing application with a feature set similar to Discord that not only features full end-to-end encryption, but also hides conversation metadata. Obscuring this metadata is important because in many cases, the contents of a given conversation matter less than the fact that a conversation occurred between two or more parties. Hackers, cyberstalkers, and leakers do not need to know the contents of communications in order to paint a clear picture of one’s associations, interests, and habits; knowing who one connects with, how long they talk for, and how often is more than enough. Therefore, we seek to protect this data.

Our implementation is a command-line Python application that allows for multiple “channels,” or independent conference calls, facilitated by a single instance of the server program. Our protocol utilizes a homomorphic encryption scheme to allow the cloud server to mix audio signals without knowing the contents of those signals or which channel a given user is in. This prevents an untrusted server from tracking who talks to one another, when they speak, and what is being said. We presume an honest-but-curious server model and utilize the Microsoft SEAL homomorphic encryption library.

FACULTY ADVISORS
Associate Professor Daniel Roche
Computer Science Department

Associate Professor Justin Blanco
Electrical and Computer Engineering Department

Associate Professor Travis Mayberry
Cyber Sciences Department


James J. Potticary
Midshipman First Class
United States Navy
 

A Novel Approach to Thermoelectric Material Fabrication Using Additive Manufacturing

Recently there has been increased interest in developing thermoelectric materials with additive manufacturing (AM) techniques. Thermoelectric materials can capture waste heat and generate electricity. These materials have not seen widespread application for several reasons including: inefficient material properties, and fabrication difficulties. AM thermoelectric materials have demonstrated lower thermal conductivities, which can be a hallmark of a more efficient thermoelectric device. AM can also be used to create difficult geometries—geometries unobtainable with standard fabrication techniques. The goal of this work was to develop and characterize an AM fabrication method capable of creating dimensionally accurate, uniform, thermoelectric materials.

N-type bismuth telluride (BiTe) was chosen as the base material due to availability and effectiveness as a room temperature thermoelectric. Initial methods of fabrication used a Formlabs Form2 Printer and a doped resin. After significant manipulation of printer parameters, a maximum concentration of 15wt% BiTe was successfully printed. Image analysis was done to verify the doping percentage. However, thermoelectric characterization showed that these samples did not exhibit a Seebeck effect and were therefore not functional thermoelectric materials. Due to the printers limitations with doped resins, two alternative methods were attempted: powder sintering in ceramic molds, and a method labeled bulk curing in plastic AM molds. In the first alternative, ceramic molds were 3D printed and thermoelectric material was sintered within the mold. Ultimately, these samples were too fragile to undergo characterization.

In the bulk curing method, BiTe doped resin was cured without the use of a printer. Instead, samples were cured in AM molds using both time and UV activated, doped resins. After the resin was cured it was burned off and the samples were sintered. The maximum concentration achieved was 80wt% BiTeSe. Once sintered, the samples exhibited a measurable thermoelectric effect. Mechanically the materials demonstrated non-homogeneous hardness characteristics due to porosity.

FACULTY ADVISORS
CAPT Brad Baker, USN
Mechanical and Nuclear Engineering Department 

Professor Peter Joyce
Mechanical and Nuclear Engineering Department 

Associate Professor Emily Retzlaff
Mechanical and Nuclear Engineering Department 

Associate Professor Hatem ElBidweihy
Electrical and Computer Engineering Department


Pippin E. Robison
Midshipman First Class
United States Navy

Investigating the Photodegradation Mechanisms of Chlorpyrifos in Arctic Lacustrine Systems

In the Arctic, organohalogen contaminants are subjected to a slew of environmental processes that affect their persistence, bioavailability, and ultimately ecological and health impacts. Due to the environmental conditions in the Arctic such as lack of canopy, increased solar irradiance in the summer, and unique organic matter, photodegradation is a critical pathway for the transformation of contaminants. Dissolved organic matter (DOM), ubiquitous to surface water, associates with poorly soluble contaminants and can affect their photodegradation. One of the most prolific organophosphate pesticides, chlorpyrifos, has been found to undergo long range transport to polar regions where it has potential to accumulate thousands of miles from application sites. Previous research indicates that the photodegradation rate of chlorpyrifos is enhanced by DOM. However, the specific role of Arctic-derived carbon pools in DOM mediated photodegradation is poorly understood. This study sought to identify and quantify the mechanistic components of chlorpyrifos’s photodegradation due to Arctic-derived DOM. DOM samples isolated from two geographically close but hydrologically different Alaskan lakes (Toolik Lake and Fog Lake) were photolyzed in the presence of chlorpyrifos by a solar simulator with probe molecules to either sensitize or quench various photodegradation mechanisms. The light screening corrected pseudo first order kinetic rates were compared to determine the overall mechanistic contribution to photodegradation extent. Seasonal differences in DOM composition were found to impact the level of DOM photosensitization. Mechanistic differences were identified for the photodegradation of chlorpyrifos in the two different DOMs. For Toolik Lake DOM at freshet, hydroxyl radical (•OH), singlet oxygen (1O2), and triplet excited state (3DOM*) electron transfer were identified as contributors to photodegradation, and •OH was found to be the primary contributor species. For Fog Lake DOM, only •OH and 1O2 were determined to contribute to photodegradation, but 1O2 was the primary contributing species. Potential transformation products were consistently observed chromatographically across multiple kinetics experiments. These products are currently undergoing analysis via mass spectrometry for identification. The mechanistic information and associated product analysis will help to better predict the fate of this contaminant and similar
compounds more broadly across Arctic systems to better understand the overall impact and potential remediation needs.

FACULTY ADVISOR
Assistant Professor Jennifer Guerard
Chemistry Department

EXTERNAL COLLABORATOR
Professor Yu-Ping Chin
University of Delaware


Logan C. Schoffstall
Midshipman First Class
United States Navy

Effects of Gamma Radiation on the Thermal and Mechanical Properties of Additively Manufactured Thermoplastics

Additive manufacturing represents a highly efficient and cost-effective solution for rapid replacement of aging parts in the defense industry. Such components are often subjected to harsh environments including exposure to radiation. While the radiation effects on conventionally manufactured engineering polymers has been studied to a limited extent, the effects on additively manufactured components of the same polymers have not been thoroughly documented. Therefore, the objective of this study is to understand the effect of radiation on the thermal and mechanical properties of high performance additively manufactured polymers. The objective was accomplished by comparing the tensile strength and thermal stability of these materials under gamma irradiation up to 20 MRad. This work is critical to potential implementation in defense applications such as the Trident missile program. Polymer properties are largely governed by their macrostructure, which includes whether they are amorphous or semicrystalline, and if they exhibit crosslinking between polymer chains. Polymers that do not inherently exhibit crosslinking are known as thermoplastics and these materials are common in additive manufacturing. Two of the most common additive manufacturing techniques are fused deposition modeling (FDM) and powder bed fusion (PBF). Both techniques involve the melting of thermoplastics and fusing successive layers until the desired shape is achieved. Results were compared to the radiation effects on injection-molded samples of the same thermoplastics. The following additively manufactured materials were tested: Nylon-12 (SLS), Ultem 9085 (FDM), NylonG – glass fiber filled nylon (FDM), and Nylforce CF – carbon fiber filled nylon (FDM). Nylon-12 and Ultem 9085 were the injection molded materials tested. Radiation doses from 0.1 up to 20 MRad were tested for each material. Thermal analysis included thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) to measure at what temperature polymer degradation occurred and enthalpy heat of fusion, respectively. Modulated differential scanning calorimetry (MDSC) was used to minimize the thermal gradients present in data. Tensile testing determined that increased radiation resulted in a decrease in tensile strength. Fractography via scanning electron microscopy (SEM) showed that there was an increase in brittle fracture present in failed specimens as the radiation dose increased. At radiation doses of greater than 10 MRad, the fracture surface exclusively exhibited brittle fracture behavior.

FACULTY ADVISORS
Professor Peter Joyce
Mechanical and Nuclear Engineering Department 

Assistant Professor Elizabeth Getto
Mechanical and Nuclear Engineering Department 

CDR David Durkin, USN
Chemistry Department

CAPT Brad Baker, USN
Mechanical and Nuclear Engineering Department 


Skyler P. Schork
Midshipman First Class
United States Navy

Machine Learning Enabled Prediction of Atmospheric Optical Turbulence From No-Reference Imaging

Laser based communication and weapons systems are integral to maintaining the operational readiness and dominance of our Navy. Perhaps one of the most intransigent obstacles for such systems is the atmosphere. This is particularly true in the near-maritime environment. Atmospheric turbulence perturbs the propagation of laser beams as they are subject to
fluctuations in the refractive index of air. As the beams travel through the atmosphere there is loss of irradiance on target, beam spread, beam wander, and intensity fluctuations of the propagating laser beam. The refractive index structure parameter, C2N, is a measure of the intensity of the optical turbulence along a path. If C2N can be easily and efficiently determined in an operating environment, the prediction of laser performance will be greatly enhanced. The goal of this research is to use image quality features in combination with machine learning techniques to accurately predict the refractive index structure parameter, C2N. In order to construct a machine learning model for the refractive index structure parameter, a series of image quality features were evaluated. Seven image quality features were selected, and have been applied to an image dataset of 34,000 individual exposures. This dataset, along with independently measured C2N values from a scintillometer as the supervised variable, were then used to train a variety of machine learning models. The models of particular interest to this research are the Generalized Linear Model, the Bagged Decision Tree, the Boosted Decision Tree, as well as the Random Forest Model. While the quantity of available training data had a significant impact on model performance, the findings indicate that image quality can be used to assist in the prediction of C2N, and that the machine learning models outperform the linear model.

FACULTY ADVISORS
Associate Professor John Burkhardt
Mechanical and Nuclear Engineering Department 

Professor Cody Brownell
Mechanical and Nuclear Engineering Department 

Associate Professor Charles Nelson
Electrical and Computer Engineering Department


Cameron B. Smith
Midshipman First Class
United States Navy

Characterizing Tandem Fin Wake Using Lateral Line Inspired Sensors

Fish have demonstrated extreme agility underwater, a desirable trait for uncrewed underwater vehicles (UUVs) seeking to perform dexterous tasks in confined environments. Much of a fish’s maneuverability can be attributed to the intricate interactions between the wakes generated by its biological control surfaces. One such interaction is between vortex wakes produced by dorsal and caudal fins. The phase difference between the oscillating fins influences the degree of thrust produced. The development of a robust feedback architecture capable of characterizing wake interaction will enable effective bioinspired vehicle motion using this phase difference.

This project replicates the lateral line organ in fish with commercially available pressure sensors and uses the lateral line’s abilities to study the downstream effects of tandem foils, which represent simplifications of a bioinspired propulsion system. As these foils oscillate with variable phase difference, resulting force data show the production of thrust or drag. The lateral line response is analyzed for features which correlate with the foil phase difference, while computational fluid dynamics simulations provide insights on the observed wake. This process shows that, for decreasing phase and thrust, the magnitude of the dominant frequencies detected by the lateral line also decrease as a result of increased space between paired vortices or destructive interference between fin wakes. A trend line is developed to relate this feature to phase difference using a polynomial fit, finding a negative correlation with a coefficient of determination of 0.575.

Sensory systems capable of estimating tandem foil phase differences can directly relate such phase differences to foil thrust production, thereby providing the basis for a bioinspired feedback control system. Ultimately, a well-functioning control system enables more robust and agile underwater locomotion, required for difficult tasks such as closely studying coral reefs, maneuvering through subsea obstacles, and operating in formation with other UUVs.

FACULTY ADVISORS
Professor Mark Murray
Mechanical and Nuclear Engineering Department 

Professor David Fredriksson
Naval Architecture and Ocean Engineering Department

Associate Professor Levi DeVries
Weapons, Robotics, and Control Engineering Department

Assistant Professor Alexander Laun
Naval Architecture and Ocean Engineering Department


Sarah G. Sorensen
Midshipman First Class
United States Navy

Ensuring Equitable Access to Liver Transplant Using Linear Programming Duality, Network Flow, and Simulation

Donor livers to transplant patients are allocated based on medical urgency and liver disease severity, via the ‘Model for End-Stage Liver Disease (MELD)’ score. The goal of allocation is to prevent candidates from dying while waiting for a liver, yet many candidates die on the list. Women are consistently 4.8% less likely to receive a liver transplant than men. Women are disadvantaged by their generally smaller abdominal cavities which cannot accommodate larger donated livers. They are also disadvantaged by lower creatinine levels; creatinine is a waste product made by the liver which signifies renal dysfunction at high levels. Since women generally have less muscle mass than men, they produce less creatinine which makes their liver disease appear less severe in the MELD score.

We propose increasing MELD scores for women, to increase their access to donated livers. To decide how many points should be added to women’s MELD scores, we created an ideal linear program for liver allocation. This linear program uses real transplant data from 2016 to test how the total MELD points and number of lives saved by an allocation of livers changes when a new constraint to enforce equity across sexes is introduced. Next, we used the duality theorem of linear programming to calculate how many points should be added to womens’ MELD scores to achieve fairness. The transplant community relies heavily on scoring mechanisms, rather than optimization, so designing an allocation rule based on a score makes it more likely to be accepted and implemented.

Next, we designed a network flow model to capture the size incompatibilities that women face when they are only able to accept small livers because of the size of their abdominal cavity. We use the Max Flow Min Cut theorem to restrict the flow of livers between small donors and large patients and create new allocation rules reserving smaller livers for smaller patients to equalize the rate of transplant between all size groups.

Finally, we tested my proposed score boost using the Liver Simulated Allocation Model (LSAM) to ensure these changes work in practice when medical details like diagnosis and physical characteristics like age, race, blood type, height, and weight are included. The simulation tested our model results by matching organs to patients one at a time, whereas the linear program and network flow model assumed future knowledge of all donated livers over the next year.

We have calculated a score boost for women to correct the bias they receive for lower natural creatinine levels and tested it with the Liver Simulated Allocation Model. We also created size restrictions using a network flow algorithm to correct for the disadvantage women have due to their overall smaller stature. Finally, we tested some of these policy changes in the Liver Simulated Allocation Model.

FACULTY ADVISOR
Professor Sommer Gentry
Mathematics Department

EXTERNAL COLLABORATOR
Associate Research Professor Nicholas Wood
Hennepin Healthcare Research Institute


Caroline G. Turner
Midshipman First Class
United States Navy

Network Analysis of Concussion Symptoms in Collegiate Athletes

Concussions are a common brain injury, affecting millions of Americans each year, including military members and athletes. Following a concussion, athletes frequently experience a wide range of consequences including various changes in neurocognitive function and psychological symptoms. As a result, the recovery process varies widely from patient to patient
with some patients recovering and returning to normal activity within 5 days while other patients experience symptoms for months. A patient’s status, is determined using multiple variables measured through testing, including changes in neurocognitive function measured using the ImPACT test and changes in psychological symptoms measured using the Brief Symptom Inventory-18. This research develops a network model that examines the relationships among these variables over time so that we can analyze how these variables are interrelated, mutually reinforcing, and amplifying in an effort to better understand the concussion recovery process.

The NCAA-DOD Concussion Assessment, Research and Education (CARE) Consortium comprehensively collects concussion test results from college athletes and service academy cadets at 30 participating institutions. These tests include baseline assessments, assessments within 48 hours of an injury, and upon reaching asymptomatic. Using the CARE dataset, we develop a network that depicts the relationships between multiple variables at individuals timepoints and the evolution of each variable over time following an injury. The model demonstrates that there are significant interactions between psychological symptoms and neurocognitive functions as a result of a concussion that were not present prior to the concussion.

We further explore the relationships between variables and the effect of this relationship on groups of individuals by grouping individuals according to recovery time and performing trajectory analysis. By developing a better understanding of which variable relationships are most impactful for different subgroups of our population, we are able to demonstrate which underlying symptoms, emergent symptoms, and grouping of symptoms most affect concussion recovery times.

FACULTY ADVISOR
Assistant Professor Anna Svirsko
Mathematics Department

EXTERNAL COLLABORATORS
Assistant Professor Gian-Gabriel Garcia
Georgia Institute of Technology

Assistant Professor Spencer Liebel
University of Utah School of Medicine

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