In this thesis, we introduce a way to implement Stochastic Processes - particularly Markov chain properties - for analyzing Liar’s Poker, a variant of Poker Texas Hold’Em that incorporates hidden information and a card-switching mechanic. Poker, and in particular Liar's Poker, presents a complex environment in which probabilities evolve as information is revealed and players make sequential decisions under uncertainty, so Markov modeling of this game requires a more flexible state-based representation. The study focuses on two main objectives: first, to construct a state space and transition matrix that are sufficiently compact for analysis while still capturing meaningful changes in hand-strength and game dynamic; and second, to investigate how the game’s exclusive card-switching feature can be incorporated into an optimal decision-making strategy. To address these goals, the thesis models gameplay as a sequence of probabilistic state transitions driven by card draws, hidden information, and strategic actions. By extending Stochastic Process methods to a poker setting with imperfect information and dynamic transition, this thesis aims to provide a structured mathematical framework for evaluating strategy in Liar’s Poker.

Incurred But Not Reported (IBNR) reserves refer to insurance claims that have already taken place, but have not yet been reported to the insurance provider. This presentation formulates a Bayesian modeling framework to estimate the IBNR reserves. The Bayesian framework allows us to incorporate prior knowledge, typically available from historical data and expert opinions, along with the observed claim data, to estimate model parameters and predict future claim liabilities. We emphasize prior models that have heavy tails and therefore can accommodate extreme, rare losses that can be underestimated otherwise. Specifically, we consider Pareto (Type I) and log-t models for the expected ultimate claim amounts for each insurance period. The data generating mechanisms considered are Poisson, negative binomial, and gamma. The analysis of real data also considers model sensitivity to the choice of the prior parameters. In doing so, we aim to produce more robust reserve estimates and better reflect the uncertainty inherent in unpaid claim liabilities. Ultimately, modeling IBNR reserves is important because it ensures insurance companies set aside sufficient funds to cover future claim obligations and avoid unexpected losses that could impact profitability.

In vitro studies are critical for elucidating the mechanisms contributing to disease development, such as how diet-induced obesity leads to increased risk and incidence of breast cancer. However, they are often limited to short-term trials which fail to mimic the prolonged exposure to energy excess that contributes to obesity development. This project investigates how acute and chronic exposure to the saturated fatty acid, palmitic acid, affects the oxidative stress response in MCF-7 breast cancer cells. In excess, palmitic acid increases cellular lipid load and can lead to the production of reactive oxygen species (ROS), ultimately resulting in inflammation and cellular damage. However, chronic exposure to low doses of oxidative stressors have been shown to be protective against acute stress events via a biologic process termed hormesis. The study compares short-term and long-term treatments to determine whether continuous exposure amplifies oxidative stress or activates cellular defense mechanisms. To do this, I have already been culturing MCF-7 cells in a low dose of palmitic acid, and will continue to do so for 3 months. Once cells have been chronically exposed to a low dose (50 µM) of palmitic acid, they will be acutely treated with a high dose (250 µM) of palmitic acid for 24-48 hr. Basal ROS production (before high dose treatment) will be compared ROS production after the high dose treatment in cells that have been chronically exposed to palmitic acid. Cells that have not been chronically exposed will serve as our controls. These studies will help us understand how chronic exposure to saturated fats, as occurs with diet-induced obesity, alters oxidative balance in breast cancer cells and contribute to a better understanding of how diet influences cancer progression and cellular stress responses.

Chylothorax is the accumulation of chyle within the thoracic or pleural cavity resulting
from thoracic duct leakage. This condition can arise from thoracic duct injury, increased
systemic pressure in the superior vena cava, and following the Fontan procedure for hypoplastic
left heart syndrome. Clinical manifestations include respiratory distress (coughing, shortness of
breath, and chest pain), milky fluid accumulation in the pleural cavity, and elevated triglyceride
and lymphocyte cell counts. Medical Nutrition Therapy (MNT) from registered dietitians is
instrumental in chylothorax management and treatment. Diet initiation is dependent on the
patients' individualized chest tube output, and strict fat restriction is vital to reduce chyle output.
General recommendations for limiting fat include <10 grams per day or <30% of total daily
calories. To prevent essential fatty acid deficiency (EFAD), which can occur within three to four
weeks of restriction, patients need a medium chain triglyceride (MCT) enriched diet and to
maintain two to four percent of calories from essential fatty acids. Signs and symptoms of EFAD
include poor wound healing, dry skin and rash, poor growth, and hair loss. Additional nutrition
concerns include increased protein requirements due to fluid losses, and the monitoring of fat-
soluble vitamins (A, D, E, K) and minerals (Calcium, Zinc) that bind to albumin. The case report
explores the complex nutrition needs, feeding timelines, and goals of care for a postoperative
chylothorax in a pediatric patient with hypoplastic left heart syndrome.

Background: Chronic stress among older adults increases risk for depression, anxiety, cardiovascular disease, and cognitive decline. Nature-based interventions may improve psychosocial and physiological stress outcomes, though longitudinal evidence in aging populations remains limited.

Methods: A convenience sample of community-dwelling older adults (N = 21; M age = 74.14 ± 4.59 years; range 65–85) participated in a six-week Nature Rx intervention study conducted in partnership with the Fort Worth Botanic Garden and Texas Christian University. The program included three two-week modules meeting twice weekly: garden yoga, forest bathing, and vegetable gardening. Repeated measures for the Well-Being/Personal Health Index (WPHI), positive and negative affect, nature-relatedness, outdoor activity minutes were assessed at baseline and at three subsequent time points across the program. Measures for handgrip strength (HGS), and salivary cortisol were assessed at the beginning of the first and sixth weeks, respectively. Friedman tests with Bonferroni-adjusted post hoc comparisons evaluated changes in psychosocial outcomes. Paired t-tests and repeated-measures ANOVA assessed physiological outcomes. Analyses were conducted using available cases due to incomplete measurements across time points.

Results: WPHI scores did not significantly change over time, χ²(3, n = 18) = 1.886, p = .596. Positive affect significantly increased, χ²(3, N = 18) = 13.437, p = .004, with higher final scores compared with baseline (padj = .012) and Post 2 (padj = .018). Negative affect also showed a significant overall time effect, χ²(3, N = 18) = 11.131, p = .011, though pairwise differences were not significant after adjustment. Nature-relatedness and outdoor minutes did not change (all p > .05). HGS remained stable, t(18) = −1.08, p = .294, and strength classification did not significantly change (Wilcoxon W = 3.00, p = .157). Salivary cortisol significantly decreased from pre- to post-intervention, t(21) = 7.653, p < .001 (d = 1.63); ANOVA confirmed a significant condition effect, F(1, 12) = 33.09, p < .001, ηp² = .734.

Conclusion: The intervention was associated with increased positive affect and statistically significant reductions in physiological stress, despite minimal changes in global well-being or muscular strength. These findings suggest short-term nature-based programs reduce stress burden in older adults. Larger controlled studies are needed to confirm these preliminary results.