VIRTUAL STUDENT SCHOLARS SYMPOSIUM 2020 PRESENTATIONS

Math and Computer Science - Poster Presentations

High School Division

Consideration of Non-Constant Viscosity in the Analysis of the Navier-Stokes Equations
Benjamin S Faktor, Canyon Crest Acadmey

In this paper, we study the question of asymptotic degrees of freedom in a
viscous flow. Particularly, we create a bound on the dimension N of the de- termining node set ξ of a fluid with time-dependent viscosity ν(t). If the fluid velocity is calculated at these N points,
the fluid velocity can be determined asymptotically over the entire domain Ω. To support the proof of this bound on N , we are required to develop some new norm inequalities. We also illus- trate how the Navier-Stokes equations, the most accepted model for the flow of a viscous fluid, arrive from physical conservation laws and properties of norms and normed spaces. For the construction of the problem, we consider a domain of Ω ⊂ Rd , d = 2 or d = 3 , a polyhedral domain which has been exactly tes- sellated with a quasi-uniform, shape-regular set of simplices. The main novelty of this paper is the creation of a bound on N that considers a non-constant viscosity (ν is replaced by the real-valued function ν(t)

Identifying Optimal Panobinostat Treatment Regimens Utilizing Reverse-Engineered Concentration-Time Curves
Jonathan C Williams, Pine Crest School

The Ex Vivo Mathematical Malignancy Advisor Model (EMMA) is a support tool for treating Multiple Myeloma. A biopsy is taken, and patient plasma cells are cultured in plates to which chemotherapies are applied. These plates are imaged, and an algorithm produces a cell viability curve for each plate. EMMA is fit to these curves, and parameterizes patient-specific models of chemosensitivity to each tested chemotherapy. For EMMA to predict patient response to a specific chemotherapy, the model must incorporate that chemotherapy’s concentration-time curves (CTCs). These describe the average temporal variation in concentration doses of a specified chemotherapy will undergo in humans. Because CTCs aren’t readily accessible to the
public, a novel mathematical model was formulated to reconstruct the CTCs of orally-administered Panobinostat. Model parameters were fit by minimizing the residual between the 20mg model curve’s c_max , t_max , and AUC_infmetrics, from those publicly provided about Panobinostat’s 20mg CTC. For the reconstructed CTCs of different doses, the model was solved using a different dosage value, and c_max , t_max , and AUC_inf were checked to ensure they fell within the reported range. Model CTCs were concatenated to create alternative treatment schedules. Using each logged patient’s chemosensitivity model, alternative treatment schedules were substituted and EMMA was run to produce best response: the predicted largest percent reduction in tumor volume that patient will experience. For 51.4% of patients, treatment scheduling produced best response metrics varied such that they were not all >50% or <5%. This indicates for half of patients, Panobinostat scheduling can be optimized.

Detecting Driver Distraction Using Neural Decoding and Machine Learning
Cleah T Winston, Homeschool

Distracted driving leads to 1,000 deaths daily in the US alone. Although current automobile safety systems exist, they do not incorporate a metric of distraction itself. The purpose of our project was to develop a machine learning-based system that decodes neural data into a measure of distraction that could be incorporated into future safety systems. To train our system, we collected electroencephalography (EEG) data using a wireless Muse headband while participants played City Car Driving. In each driving trial, the participant was presented either with no distraction or a randomly chosen distraction. We used data processing techniques, to normalize and reduce noise in our dataset, and tested supervised machine learning models to decode relative frequency band powers into distraction. For binary classification to detect whether an individual was distracted, we tested a logistic regression model (71.3% accuracy) and a multilayer perceptron (81.2% accuracy). Next, we designed a distraction metric on a scale of 0 to 5. We implemented a multivariable linear regression (mse = 0.93), and a decision tree classifier (71% accuracy) to predict this metric. The multilayer perceptron most effectively detected the presence of distraction, and the decision tree best predicted distraction level. Using recursive feature elimination, we determined that the delta and beta frequency bands drove our classifier performance. With this research, we demonstrated that a commercially available wireless EEG system can accurately decode neural data into distraction. Our EEG-based early driver distraction detection system has the potential to be incorporated into safety systems to improve driver safety.

Undergraduate Division

Integrating and Visualizing Crash Data for Trip Planning
Xavier Doh, Kean University

Technology significantly evolves over the time in a way that almost everyone relies on GPS-based navigation systems in their daily commute to navigate from one place to another. In order to select the best possible way for a user to get from location A to B, some decision factors include the ETA (Estimated Time Arrival) and/or the shortest distance needed to get to the destination.
However, in the route selection decision-making process, other factors such as the distribution of “accidents that occurred along a route” are not incorporated. For instance, studies show that women and elders have more chances to select safer routes than to faster routes. This study integrates navigation systems to visually display a real time risk level of accidents that occurred, including the type of accident frequently involved on the selected road to keep the drivers notified and attentively pay attention to the road laws in order to safely get to their destinations, or even avoid those routes.
In detail we develop a web-based navigation system using Google Maps Platform along with data on Motor Vehicle Collision Reports for New York capable of displaying this information. The system has two main functions: a data visualization of previous collisions based on their location and a display of collision along the selected road of the map. On top of that, the system counts each collision to make a report notifying about their frequency on each street. We develop this powerful information system based on the advanced web development tools.

VIRTUAL STUDENT SCHOLARS SYMPOSIUM 2020 PRESENTATIONS

Math and Computer Science - Poster Presentations

High School Division

Undergraduate Division

About

Programs

Chapters

Meetings & Events

Members

News

Publications