Brianna Gawronski, AMT495: Applied Mathematics Project
Faculty Mentor(s): Professor Saziye Bayram, Mathematics, Professor Derek Beahm, Biology
Cell volume dynamics can be influenced by many different factors in a cell, such as the diffusion of osmotically active compounds between the cell and the extracellular environment via transport proteins. Gap junctions are protein complexes made from the interaction of two connexon half-channels, which create a bridge between two cells to connect their cytosolic compartments. In our study, we explore a heterogenous syncytium of two clones of CHO cells connected by gap junctions, one that overexpresses a gene for aquaporin channels and one that overexpresses a gene for a control protein. The aquaporin cells (CHO-AQP) swell much faster than the control cells (CHO-CD81) when perfused with hypotonic media. Under these conditions, excluding ion transport through the plasma membrane and cell stress factors, we propose a simplified mathematical model, describing the volume dynamics between the syncytium, propagated by the connection specifically during the initial ten seconds of exposure to hypotonic media. Our model is derived from the effects of the induced junctional gradient, driven by the non-uniform increase in water concentration between the two cell compartments. Different cases that have been suggested as the activity are considered and used to estimate and fit data from the relative volumes and concentrations of the coupled cells before the regulated volume decrease begins to occur (tens of minutes after perfusion in hypotonic media).
Erinanne Gueli, AMT495: Applied Mathematics Project
Faculty Mentor(s): Professor Chaitali Ghosh, Mathematics
Burn injuries continue to be one of the leading causes of unintentional death and injury in the United States, and the primary causes are fire-flame, scalds, contact with a hot object, electrical and chemicals. In the United States, around 1.1 million burn injuries require medical attention annually. Approximately 50,000 require hospitalization and approximately 4,500 of those people die. In addition, a large number of people die from burn-related infections every year. Children under the age of 15 are more vulnerable to scald burns, and fire-flame burn risk increases as age increases for the general population. Burn injuries are a major public health concern since many of the survivors sustain serious scarring, and life-long physical and emotional disabilities. Addressing these factors is important to help us understand survival in burn injuries. This project aims to identify the factors that predict the likelihood of survival in a burn center using an observational study of 1000 patients obtained from the National Burn Repository. Potential predictors such as age, gender, race, total burn surface area, burn involved inhalation injury, and flame involved inhalation injury will be considered using standard statistical analysis.
Dawn Jones, AMT495: Applied Mathematics Project
Faculty Mentor(s): Professor Bruce Swan, Mathematics
Drug addiction has been a rampant problem across the United States since the late 1800's. Although some individuals have successfully completed drug rehabilitation programs, some patients found these programs unsatisfactory. According to Vertava Health, this can be frequently attributed to lack of engagement, especially when a patient is admitted unwillingly. Additionally, many rehabilitation programs do not have the necessary resources to provide personalized guidance. By utilizing a regression model, we analyze a dataset based on addict's health from their own point of view. The results from our analyses could advise healthcare professionals on how to narrow treatment options efficiently for patients who abuse a specific substance, in order for them to have a successful recovery.
Brendon Kendall and Robert DiBenedetto
Brendon Kendall, Robert DiBenedetto, AMT495: Applied Mathematics Project
Faculty Mentor(s): Professor Joaquin Carbonara, Mathematics
In this project, we gather tweets and other social media comments that mention publicly traded companies. Then we quantify the positive or negative sentiment of each comment using Artificial Intelligence (AI) tools. This AI field of study is usually referred to as Natural Language Processing (NLP). In order to obtain these comments, API accounts were created from Twitter and other companies. The quantified sentiments of the comments will be compared with stock values to determine correlation and other statistical properties. Visualization of the data will be used to further derive properties. News stories like the controversy over GameStop's stock market saga will be explained in the context of our statistical research.
Mistral Khan-Becerra, AMT495: Applied Mathematics Project
Faculty Mentor(s): Professor Hongliang Xu, Mathematics
Endeavors in efficiency and production improvements are frequently met with trepidation and fear from the general workforce. It does not help that this culture is sometimes bolstered by internal resistance for change and poor management. In this project, a compromise will be explored on a micro-level that may be applicable to larger systems, with larger workforces. We first identify a simplified set of products, quantify the tasks involved to produce each, and, with the use of multiple simulations, we measure the level of complexity arising from different running orders. From here, we define a model which could aid management in determining how large a crew is needed to run different schedules of product. The machine we discuss, in particular, is a slitter, used to slit flat rolled copper and brass coils. The crew normally consists of four operators, we explore what production schedules would merit those four operators and which could be run with only three, freeing the fourth to work elsewhere, or train on new skills.
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