Crafts and Conversations collaborates with Trinity Terrace and Brookdale assisted living facilities to foster a connection between TCU students and the residents living there. Through monthly meet ups with crafts and music, inter-generational relationships are built between students and residents. Crafts such as painting with mini easels or making yarn octopi provide a base talking point that expands into other natural parts of conversation, such as telling stories. Students that volunteer at crafts gain friendships, valuable interactions that combat stereotypes against the elderly, and improved communication skills. Additionally, students have the opportunity to perform music, enabling them to further expand their creativity. Residents at assisted living facilities also gain valuable friendships and interactions that combat the potential loneliness of at a retirement center. Crafts and Conversations strives to enrich the lives of all those involved through engaging activities that bring people closer together.

Beautiful Feet Clinic, founded by Dr. David Capper, provides free medical, dental, and holistic care for individuals experiencing homelessness in Southside Fort Worth. One of the critical challenges faced by individuals experiencing homelessness is the lack of access to preventive screenings, flu vaccinations, and health education, leading to the late detection of chronic illnesses such as diabetes, hypertension, and cancer. Many patients at Beautiful Feet Clinic do not routinely engage in preventive care, as their immediate survival needs—such as securing food and shelter—often take precedence over long-term health maintenance. Without timely interventions, undiagnosed and unmanaged chronic illnesses contribute to higher emergency department utilization, increased morbidity, and worsening overall health outcomes.

To address this gap, we partnered with Lauren, a medical student at TCOM, to offer flu vaccinations and organize a Community Health Screening Day on March 29th, 2025, offering essential health screenings and practical nutrition education aimed at empowering individuals experiencing homelessness to improve chronic disease management and overall well-being. Patients will learn simple meal modifications to make healthier choices within their available food options through educational pamphlets with a focus on nutritional education to reduce chronic illnesses. The event also enhances medical student training, with efforts to secure an OB-GYN physician to guide manual breast exams and oversee preventive education regarding breast and skin cancer screenings. The initiative also administered 22 flu vaccinations to address gaps in preventive care, reducing the risk of seasonal influenza among unhoused individuals who face significant healthcare barriers. Additionally, in collaboration with Moncrief Cancer Institute, a mobile cancer screening clinic, we will provide free cancer screenings in summer 2025, to promote early detection for at-risk individuals.

Beyond medical care, Beautiful Feet Clinic also faces communication barriers with Spanish-speaking patients, limiting access to critical health services. Many patients and healthcare providers recognize the need for language accessibility and the importance of qualified interpreters in delivering effective care. To address this, we translated the clinic’s intake forms into Spanish and established a list of medical students proficient in Spanish who can assist with interpretation over the phone. This initiative enhances provider-patient communication, ensuring that Spanish-speaking individuals receive accurate medical information and compassionate care.

By integrating screenings, outreach, language accessibility, and hands-on clinical training, this initiative fosters health empowerment and long-term community-based healthcare solutions. It emphasizes collaboration between healthcare institutions, students, and local clinics to bridge gaps in care for vulnerable populations.

Geodesic nets are types of graphs in Riemannian manifolds where each edge is a geodesic segment. One important object used in the construction of geodesic nets is a balanced vertex, where the sum of unit tangent vectors along adjacent edges is zero. We prove the existence of a balanced vertex of a triangle (with three unbalanced vertices) on a general two-dimensional Riemannian surface when all angles measure less than $2\pi/3$, if the length of the sides of the triangle is not too large. This property is a generalization for the existence of the Fermat point of a planar triangle.

The Cheeger’s constant, also known as the isoperimetric number, is a constant that helps describe the bottleneck present in a graph, if any. Some fields, such as computer networks, have an interest in this constant due to the application of the constant in their field. We examined randomly generated connected graphs and their isoperimetric numbers by developing algorithms to calculate it.

One of the major challenges in education is accurately quantifying a student’s knowledge and skills. Since we cannot directly measure a student’s true intelligence, we rely on test performance, which serves as an imperfect representation of their abilities. This issue arises in many statistical applications where the key problem involves a population in which each individual possesses an underlying ability or trait that cannot be directly observed but can only be inferred through proxy variables. However, these proxies are often contaminated, providing only a noisy or imperfect approximation of the true latent variable.
This project focuses on techniques for recovering latent variables from noisy data. In this context, "recovery" refers to estimating the latent variable using indirect observations. Assuming a linear relationship between the latent trait and the observed proxy variables, we can estimate model parameters and subsequently recover the values of the latent variables.
Specifically, we will examine statistical approaches to latent variable recovery when the test contains items that exhibit differential item functioning (DIF). This means that certain test items do not solely measure the intended knowledge or ability but are also biased toward specific groups. The objective is to develop methods that detect the presence of DIF and adjust for it, allowing for a more accurate estimation of the underlying abilities.
To illustrate these methods, we will use the Holzinger-Swineford dataset, a well-known dataset in psychometrics used to analyze cognitive abilities across multiple domains. This dataset includes 88 observations with scores in five areas: Mechanical Comprehension, Verbal or Visual Comprehension, Algebra Operations, Analytical Operations, and Statistical Reasoning. By applying a linear contamination model, we aim to recover each student's latent ability while accounting for DIF.